ARD Client available after restart-Then become grey (unavailable) can ping

In the past couple of months, I have started having problems with one of the Mac I manage remotely. Upon restarting the Mac running 10.5.6 it is available remotely. As time passes (hours) I get the gray icon for this iMac when I view it from Apple Remote. The iMac has the ARD Client 3.2.2 update installed. I can ping this computer successfully. I checked to be sure no firewall in enabled. I verified that computer and display are set to sleep never. Hard drive is allowed to sleep. A screen saver does start after a short while (15 min I think). The only thing I know to try next is to uninstall ARD Client 3.2.2 and reinstall per instructions I've seen elsewhere.

Incidentally, I last week I installed "Logmein" to allow remote access so I could restart the computer when Apple Remote was not working. That too becomes unavailable when ARD client is unavailable. So when ARD client is active I can access the computer by either Apple Remote or Logmein. When ARD is inactive, neither work.

Any other ideas about what is going on?