I wonder if your ISP has a complete understanding of the terms?
Wikopedia (which can hardly be seen as biased to Microsoft) directs the request for Web Farm to the definition of Server Farm:
Server farms are commonly used for cluster computing. Many modern supercomputers comprise giant server farms of high-speed processors connected by either Gigabit Ethernet or custom interconnects such as Infiniband or Myrinet.
Another common use of server farms is for web hosting, which are sometimes referred to as web farms.
Anyway enough semantics, you need to find out from your ISP if your DNN site is indeed being hosted on multiple servers and if it is, then are the files being replicated between the webheads or are they pointing to a common file share?
Your original question/problem had to do with the Remember Me cookie, but are you seeing any issues with changes to the site being delayed? In other words if you edit a module and then refresh the page do your edits show up immediately? If the only problem is that Remember me is working sporadic then you might need to look elsewhere. Remember Me sets a cookie so maybe something is in the cookie and when your user hits another server in the "WebFarm" that server is not recognizing the cookie information. Hopefully there are some cookie experts who might chime in on this.
There are many posts about Remember Me:
http://www.snapsis.com/DotNetNuke/Support/tabid/560/aff/10/aft/5813/afv/topic/Default.aspx
http://www.dotnetnuke.com/Community/Blogs/tabid/825/EntryId/1704/Why-doesnt-Remember-me-work-like-I-expect.aspx
http://dnnblog.venexus.com/DotNetNuke+4+Persistent+Login+Remember+Me+For+More+Than+1+Hour.aspx