I would first take it apart and see if the gears are binding when they turn. Are the bearings, where the shaft for the gears are in, are they loose?
If everything seems ok, then clean off the old grease and use something like that white grease, lubriplate i believe. It turns so slow almost any grease would work. ie, better than no grease at all.
But, the brushes on the electric motors could be shot too. Or the bearings on the motor. Does it dose every day? for 5 years?
So hard to say, long distance and all

They are 5 years old but have only seen regular use for about half that time.

Well hopefully you will get an email back from the co.
But if it is going to cost you to buy a new part, then you have to take it apart anyway. Then maybe the problem will be more apparent and you will be able to fix it yourself.

OK, so I heard back from the president and he suggested basicaly the same things as you guys. I took one of the pumps apart and the grease inside is copious and dried up like a very thick paste. So I'll get some grease and try regreasing both of the pumps first. I'll update to let everyone know how it worked out.

Thanks for your insight, by the way. Sounds like you know a thing or two about peristaltic pumps! Where would you get lubriplate?

One pump was used for top-off so it was every day for at least 2 to 3 years. The other was barely used at all, just for dosing calcium once a day for about 3 years. Oh, come to think of it, that pump was also used to pump water into my denitrator (or out of it, I can't remember!)

Try and get all the old grease off before you put in new. If it is easy to detach the gearbox, then you could wash it in varsol,
Just make sure then the new grease gets into whatever they use for bearings.
Good luck