AC will only work in the early morning.

AC will only work in the early morning.

I recently moved into an old home with 2 identical AC units, the one on the west side of my house only works during the early morning and will not respond during the day. I have had an AC repair person come in in the morning and it was working fine therefore he cannot find any problems. I've swaped the thermostats on the wall and it is doing the same thing, so it will not be a thermostats issue.

Any suggestions?