Unable to login

Ever since upgrading to OS X Maverick I am having issues with logging in with my account and the same for other peoples accounts. After entering the correct password all I get is the shaking / nodding indicating incorrect password. Same for my wife with her account. The password I am using is correct - becasue sometimes I can login and then sometimes it does not permit me to login. The only way to fix this is to restart with Option-Command-P-R keys held down. Then I have to re-install OS X.

This is an intermittent issue and seems to happen every 2 or 3 days.

I have a early 2009 IMac (Intel).

I replaced the PRam battery but this did not make any difference. I cant find any similar incidents so I am at a loss on how to fix this. Any assistance / ideas would be appreciated.

Simon