1999 Pontiac Sunfire Starter issue (I think)

I bought this car used. It has 190k on it. Runs awesome. Had some minor things to
repair when I got it one of those being the starter motor. We had a situation where,
when turning the key to start the car, nothing would happen. Batt was good as well.
After numerous attempts it would finally turn the starter to start the car. Then it
reached a point where we felt the starter simply crapped on us. Figuring it was the
solenoid so replaced the whole starter.

After replacing the starter all was good. Has been a couple months now and it looks
like the same thing is starting to happen. In fact, in happened the same day of this
posting. I am stuck as to what it could be. I did tap on the solenoid a bit the first time
and it started after that. This a two weeks before this time. When leaving work today,
same thing, turn the key, starter doing nothing. Batt is fully charged. I tap on the
solenoid a few times but in about 5 or so consecutive rounds and finally it starts. Now,
when it was doing this before starter replacement, I never tapped on the solenoid. So I
personally can't relate the two. Any thoughts into what direction to go in would be
great. I think the starter is under warranty still but I don't think the starter is bad. It has
to be something else. Thanks.