What is it that doesn't happen every time?

I had the same problem. I had to change the code. Did it by opening the transmitter (the button in your car). there should be a series of slide switches preset at the factory. you can change these to whatever you like.
It doesn't matter what you set them to as long as ALL transmitters and especially the opener in the garage is changed to the same code. On the opener there should be a plastic cover that pops off to reset the code.

Newer door openers actually have a "rolling code" feature to prevent this problem

I would file a complaint with the property managers. Their continued use of those old openers is putting you at risk. They should upgrade those openers to new rolling code models right away.

Ask the landlord if he realizes how much it will cost him if something happens to you or your property if he doesn't replace the unit after you have informed him of the problem.