I seem to have runaway logs associated with the scheduler.

DNN version 4.8.2

 Type Enabled Frequency Retry Time Lapse Next Start
Enabled:  
  DotNetNuke.Entities.Users.PurgeUsersOnline, DOTNETNUKE   Every 1 Minute  Every 5 Minutes  4/1/2008 6:29:26 PM  History 
  DotNetNuke.Services.Log.SiteLog.PurgeSiteLog, DOTNETNUKE  Every 1 Day  Every 2 Hours   History 
Enabled:
  DotNetNuke.Services.Scheduling.PurgeScheduleHistory, DOTNETNUKE   Every 1 Day  Every 2 Days  4/2/2008 1:43:30 AM  History 
  DotNetNuke.Services.Log.EventLog.PurgeLogBuffer, DOTNETNUKE  Every 1 Minute  Every 5 Minutes   History 
  DotNetNuke.Services.Log.EventLog.SendLogNotifications, DOTNETNUKE  Every 5 Minutes  Every 10 Minutes   History 
Enabled:
  DotNetNuke.Services.Search.SearchEngineScheduler, DOTNETNUKE   Every 30 Minutes  Every 60 Minutes  4/1/2008 6:29:35 PM  History 
  DotNetNuke.Modules.Admin.ResourceInstaller.InstallResources, DOTNETNUKE  Every 30 Minutes  Every 60 Minutes   History 
  DotNetNuke.Services.FileSystem.SynchronizeFileSystem, DOTNETNUKE  Every 1 Hour  Every 2 Hours   History 
  DotNetNuke.Services.Cache.PurgeCache, DOTNETNUKE  Every 2 Hours  Every 30 Minutes   History 
  YAP.EmailManager.Common.EmailScheduler, YAP.EmailManager  Every 5 Minutes  Every 15 Minutes   History 

These are the only three checked as enabled.
  DotNetNuke.Entities.Users.PurgeUsersOnline, DOTNETNUKE   Every 1 Minute  Every 5 Minutes  4/1/2008 6:29:26 PM  History 
  DotNetNuke.Services.Scheduling.PurgeScheduleHistory, DOTNETNUKE   Every 1 Day  Every 2 Days  4/2/2008 1:43:30 AM  History 
  DotNetNuke.Services.Search.SearchEngineScheduler, DOTNETNUKE   Every 30 Minutes  Every 60 Minutes  4/1/2008 6:29:35 PM  History 

4/1/2008 6:25:45 PM   Scheduler Stopped        ... 
Server Name: RSNET2
 
 
 
   4/1/2008 6:25:44 PM   Debug Info       EVENT NOT RUN REASON: Task not run because task is scheduled for 4/ ... 
EVENT NOT RUN REASON: Task not run because task is scheduled for 4/1/2008 6:29:35 PM
SCHEDULE ID: 6
TYPE FULL NAME: DotNetNuke.Services.Search.SearchEngineScheduler, DOTNETNUKE
Server Name: RSNET2
 
 
 
   4/1/2008 6:25:44 PM   Debug Info       EVENT NOT RUN REASON: Task not run because task is scheduled for 4/ ... 
EVENT NOT RUN REASON: Task not run because task is scheduled for 4/2/2008 1:43:30 AM
SCHEDULE ID: 3
TYPE FULL NAME: DotNetNuke.Services.Scheduling.PurgeScheduleHistory, DOTNETNUKE
Server Name: RSNET2
 
 
 
   4/1/2008 6:25:44 PM   Scheduler Started        ... 
Server Name: RSNET2
 
 
 
   4/1/2008 6:24:48 PM   Application Shutting Down       Shutdown Details: The AppDomain shut down because of the hosting env ... 
Shutdown Details: The AppDomain shut down because of the hosting environment.
Server Name: RSNET2
 
 
 
   4/1/2008 6:24:33 PM   Debug Info       EVENT ADDED TO PROCESS GROUP 0: DotNetNuke.Entities.Users.PurgeUsers ... 
EVENT ADDED TO PROCESS GROUP 0: DotNetNuke.Entities.Users.PurgeUsersOnline, DOTNETNUKE
SCHEDULE ID: 1
Server Name: RSNET2
 
 
 
   4/1/2008 6:24:33 PM   Scheduler Stopped        ... 
Server Name: RSNET2
 
 
 
   4/1/2008 6:24:33 PM   Debug Info       EVENT NOT RUN REASON: Task not run because task is scheduled for 4/ ... 
EVENT NOT RUN REASON: Task not run because task is scheduled for 4/2/2008 1:43:30 AM
SCHEDULE ID: 3
TYPE FULL NAME: DotNetNuke.Services.Scheduling.PurgeScheduleHistory, DOTNETNUKE
Server Name: RSNET2
 
 
 
   4/1/2008 6:24:33 PM   Debug Info       EVENT NOT RUN REASON: Task not run because task is scheduled for 4/ ... 
EVENT NOT RUN REASON: Task not run because task is scheduled for 4/1/2008 6:29:35 PM
SCHEDULE ID: 6
TYPE FULL NAME: DotNetNuke.Services.Search.SearchEngineScheduler, DOTNETNUKE
Server Name: RSNET2
 
 
  4/1/2008 6:24:33 PM   Scheduler Stopped        ... 
Server Name: RSNET2
 
 
 
   4/1/2008 6:24:33 PM   Debug Info       EVENT NOT RUN REASON: Task not run because task is scheduled for 4/ ... 
EVENT NOT RUN REASON: Task not run because task is scheduled for 4/2/2008 1:43:30 AM
SCHEDULE ID: 3
TYPE FULL NAME: DotNetNuke.Services.Scheduling.PurgeScheduleHistory, DOTNETNUKE
Server Name: RSNET2
 
 
 
   4/1/2008 6:24:33 PM   Debug Info       EVENT NOT RUN REASON: Task not run because task is scheduled for 4/ ... 
EVENT NOT RUN REASON: Task not run because task is scheduled for 4/1/2008 6:29:35 PM
SCHEDULE ID: 6
TYPE FULL NAME: DotNetNuke.Services.Search.SearchEngineScheduler, DOTNETNUKE
Server Name: RSNET2
 
 
 
   4/1/2008 6:24:32 PM   Scheduler Started        ... 
Server Name: RSNET2
 
 
 
   4/1/2008 6:24:31 PM   Application Started        ... 
Server Name: RSNET2
 
 
 
   4/1/2008 6:23:13 PM   Debug Info       EVENT NOT RUN REASON: Task not run because task is scheduled for 4/ ... 
EVENT NOT RUN REASON: Task not run because task is scheduled for 4/2/2008 1:43:30 AM
SCHEDULE ID: 3
TYPE FULL NAME: DotNetNuke.Services.Scheduling.PurgeScheduleHistory, DOTNETNUKE
Server Name: RSNET2
 
 
 
   4/1/2008 6:23:13 PM   Scheduler Stopped        ... 
Server Name: RSNET2
 
 
 
   4/1/2008 6:23:13 PM   Debug Info       EVENT NOT RUN REASON: Task not run because task is scheduled for 4/ ... 
EVENT NOT RUN REASON: Task not run because task is scheduled for 4/1/2008 6:29:35 PM
SCHEDULE ID: 6
TYPE FULL NAME: DotNetNuke.Services.Search.SearchEngineScheduler, DOTNETNUKE
Server Name: RSNET2
 
 
 
   4/1/2008 6:23:13 PM   Debug Info       EVENT ADDED TO PROCESS GROUP 0: DotNetNuke.Entities.Users.PurgeUsers ... 
EVENT ADDED TO PROCESS GROUP 0: DotNetNuke.Entities.Users.PurgeUsersOnline, DOTNETNUKE
SCHEDULE ID: 1
Server Name: RSNET2
 
 
 
   4/1/2008 6:23:12 PM   Scheduler Started        ... 
Server Name: RSNET2

same here but slightly different..  thousands of these

InnerException: The INSERT statement conflicted with the FOREIGN KEY constraint "FK_SearchItemWordPosition_SearchItemWord". The conflict occurred in database "spbdb", table "dbo.SearchItemWord", column 'SearchItemWordID'. The statement has been terminated.
FileName:
FileLineNumber: -1
FileColumnNumber: -1
Method:
StackTrace:
Message: System.Data.SqlClient.SqlException: The INSERT statement conflicted with the FOREIGN KEY constraint "FK_SearchItemWordPosition_SearchItemWord". The conflict occurred in database "xxxxx", table "dbo.SearchItemWord", column 'SearchItemWordID'. The statement has been terminated. at System.Data.SqlClient.SqlConnection.OnError(SqlException exception, Boolean breakConnection) at System.Data.SqlClient.SqlInternalConnection.OnError(SqlException exception, Boolean breakConnection) at System.Data.SqlClient.TdsParser.ThrowExceptionAndWarning(TdsParserStateObject stateObj) at System.Data.SqlClient.TdsParser.Run(RunBehavior runBehavior, SqlCommand cmdHandler, SqlDataReader dataStream, BulkCopySimpleResultSet bulkCopyHandler, TdsParserStateObject stateObj) at System.Data.SqlClient.SqlCommand.FinishExecuteReader(SqlDataReader ds, RunBehavior runBehavior, String resetOptionsString) at System.Data.SqlClient.SqlCommand.RunExecuteReaderTds(CommandBehavior cmdBehavior, RunBehavior runBehavior, Boolean returnStream, Boolean async) at System.Data.SqlClient.SqlCommand.RunExecuteReader(CommandBehavior cmdBehavior, RunBehavior runBehavior, Boolean returnStream, String method, DbAsyncResult result) at System.Data.SqlClient.SqlCommand.InternalExecuteNonQuery(DbAsyncResult result, String methodName, Boolean sendToPipe) at System.Data.SqlClient.SqlCommand.ExecuteNonQuery() at Microsoft.ApplicationBlocks.Data.SqlHelper.ExecuteNonQuery(SqlConnection connection, CommandType commandType, String commandText, SqlParameter[] commandParameters) at Microsoft.ApplicationBlocks.Data.SqlHelper.ExecuteNonQuery(String connectionString, CommandType commandType, String commandText, SqlParameter[] commandParameters) at Microsoft.ApplicationBlocks.Data.SqlHelper.ExecuteNonQuery(String connectionString, String spName, Object[] parameterValues) at DotNetNuke.Data.SqlDataProvider.AddSearchItemWordPosition(Int32 SearchItemWordID, String ContentPositions) at DotNetNuke.Services.Search.SearchDataStore.AddIndexWords(Int32 IndexId, SearchItemInfo SearchItem, String Language) at DotNetNuke.Services.Search.SearchDataStore.StoreSearchItems(SearchItemInfoCollection SearchItems)

If I had to guess, I'd think you have a bad index. You might search and see if there is a way to rebuild/force a search. If you figure it out, let me know, since I think I'll have to do that after I get these issues solved.