I am having a problem that has been popping up recently (past few weeks), where my login attempts through putty would timeout. Going into VMware, my attempt to login through console, with a local admin account, were also timing out. Since I was unable to access the VM, I decided to reboot the server and both login methods were restored. A day or two later, the problem had returned. I have not been able to find anything in the logs.

Anyone have any ideas on what I could check to see why or how all login attempts are timing out? And what does rebooting the VM clear out to restore them?

You might check to see if a value for the variable TMOUT is being set.
See the TMOUT section of the bash man page.

There is not a TMOUT value set within bash.