Mail program is inconsistant the longer it runs the more connection problem

Mail program is inconsistant the longer it runs the more connection problem. When I first sign on it usually connects and I can receive and send mail but within a few minutes it tells me it is unable to connect or send mail out. I've changed my gmail accounts multiple times and reinstalled them both letting apple mail do it and doing it manually. Nothing helps. I changed from gmail pop to ipop. No luck. My other account aol.com is having trouble as well. When I use firefox to access these accounts no problems.

I don't know if this is related but at the same time, Safari slows down and at time indicates I can't connect to a server while I am on Firefox ( at the same time) I have no problems.

I went back in time machine to two weeks ago and reloaded mail and that did not help. TimeMachine will not allow me to reload and older version of Safari.

this happens on both my laptop and desktop - started around Dec 28th or so.