i had similar problems with odbc ... on windows server 2003.
The fm server console told me that odbc was running and healthy (green dots everywhere), but a netstat and tcpview told me that port 2399 didn´t reply a single bit.
De- and reinstalling fm server didnt help, only a clean and slim reinstallation from scrap (starting with w2k3) got odbc to work.
In your case i would suggest a regular reboot once a week. At a time, where (when?) you have the least (or none) traffic on your server. Maybee midnight would be a good time to do.
greetings from germany