Yes. You had time quotas, typically.

Downloading files might also be limited by an upload/download ratio restriction, too.

A friend of mine wrote an external program for a particular BBS (what were colloquially known as "door" programs-- software adjunct to the BBS that remote callers could interact with) that allowed you to "bank" your quota time.

Time banks were fairly common. For those with slower modems, it was sometimes the only way you would be able to download an entire program. File downloads were not always resumable back then, depending on the transfer protocols supported by your terminal software and/or the BBS.