New battery and starter, but car doesn't start every time. What could be the problem?

For the past four years, my car wouldn't start in cold weather, but jumping it would start it up right
away. In the past couple of months, the car would randomly not start the second time around even
in warm weather. For example, I'd come out of the house and start it for the first time, which
always worked, but then I would drive somewhere, turn the car off, and then try to start it a second
time, and nothing. But jumping worked. So, I had the battery replaced, along with a corroded
cable, and it seemed to work fine for a week.

But then, it just stopped working completely. I would turn the key to the start position, and the
dashboard lights came on. The first couple of times, there was a clicking sound, and then nothing.
Since jumping didn't help, I had it towed to my very trustworthy auto shop, and it concluded the
problem was the starter. They did a very thorough assessment since my bf and his father had
looked over the car and thought it could be electrical but the mechanics found nothing else wrong
with it. So, I had that replaced, and when I went to pick it up, it worked perfectly. The next day, I
go to turn on the car, and it does so veerrry reluctantly. I turn it off, then turn the key to the start
position again, and absolutely nothing; the dashboard lights come one, and there's no clicking. I
leave it for a couple of hours to run some errands, and when I come back, I decide to try one more
time, and this time it starts up just fine, so I hightail it to the auto shop.

I've already gone through the two most obvious solutions, and I can't really afford any more repairs
for now unless the fix is really inexpensive. So I'm wondering what I should expect as far as the
possible causes? Thank you in advance for your input!