These drives and tapes are really quite old now, and they're a format that has a particular problem:
QIC tapes have an internal rubber belt that is used to drive the reels of tape, and it degrades with time. There's some variety to the failure modes of rubber (some get hard and crack, others stretch with no other visible problem, and some turns to sticky goo that gets on everything) but the general idea is that very few tapes of this format are working out of the box these days. In a scenario where you absolutely must recover the data on a tape, there are ways to 'fix' the tape long enough to read it into a modern PC, but these generally shouldn't be considered to be a viable backup option anymore.
The other common failure points in the drives themselves are the rubber parts there: belts, and the pinch roller (at least I think QIC uses a pinch roller).
I believe Meridian Mail uses SCSI tape drives, so there may be something a bit more reliable that could be swapped in for backups, but it's down to whether the OS that Meridian Mail runs on is generic enough with SCSI tape support that it would work with a different drive. There's also a few modern devices that support tape emulation, even Nortel used some of them in the DMS-100 to replace the aging DDS tape format in a few places.
At this point, something as old as Meridian Mail is frankly getting into the vintage computing era of electronics equipment, and you might have to look to some of the techniques that community uses to keep these old systems going.