Do you know how to run sde command line? If so, try this:
sdeconfig -o alter -v TCPKEEPALIVE=TRUE -i esri_sde -u sde -p password
when it asks you if you want to update, type Y for yes.
Assumptions: esri_sde is the name of your ArcSDE service, sde is the name of your sde account, password is your sde account password
Ok, after some consideration, this might not be your problem. This fixes orphaned gsrvr processes which would result from ArcIMS or ArcGIS Server connections that time out. You didn't mention either of those products, so this is probably bad advice. Forget I said anything.