Like anything mechanical or electrical, parts can die, wear out or malfunction. While I am not aware of a lot of reports of failures of TPM Monitors or sensors I would be surprised if the only problems were related to battery life or improper set-up.
This post is limited to TPMS that use externally mounted sensors. i.e. the ones that screw onto the end of your valve stem.
Batteries. They eventually will die. The early warning of loss of signal from a sensor that previously was working appears to be an occasional intermittent loss of signal, followed eventually by almost constant no signal on the display. This is easy to fix as most of these systems have user replaceable batteries. I always carry a couple but also I don't stock up as batteries may lose power even sitting in their original packaging.
"O" ring: Under the screw-on plastic cap there is a very small O-ring. As with any rubber component they can simply die ( crack or tear) just from normal use as rubber does "age-out" due to exposure to heat an Ozone in the atmosphere. I would suggest having a few "O" rings on hand as, unlike the batteries, you can't just pick up a replacement at CVS, Walmart, or Walgreens. You will probably have to get them from your TPMS dealer. When you screw the cap on the sensor don't overtighten the cap as that can distort the O-ring and shorten its life
Plastic cap. This part should last longer than the rubber O-Ring but plastic ages too. Again this is special and unique to your brand TPMS so having at least one on hand from your dealer is a good idea. Also, don't over tighten the cap. It might be possible to seal a cracked cap for a short time with Silicone seal or glue but be careful not to glue the cap to the sensor.
Sensor electronics. All you can do here is get a new replacement sensor. Some brand TPMS offer a longer-term warranty (Lifetime) others only 12 months. I do carry a spare sensor but not in my toolbox or parts box but I added a sensor to my spare tire. in my Class-C. This gives give me a replacement I could use on a ground tire if one of those sensors ever failed. It would only require a quick program change when I move the sensor from a spare position to the ground tire. I could do without a sensor on the spare for the week it might take to get a replacement sensor. The reputable dealers I have talked with all offer single sensor sales or replacement under warranty. A sensor on a spare tire would probably last longer than the other external sensors as it isn't exposed to potential strike from road debris or heat from the tire or brake drum. If I had a sensor fail I would plan on keeping the cap and O-ring if in good condition as a future spare part.
Monitor. Well if this part fails I don't know of any repair a user could do. You just need to get a new monitor from your dealer and hope you have a good warranty and that your dealer will sell the monitor by itself so you don't have to buy another complete system. I have to admit that I did manage to damage my older monitor after four years of reliable use. I grabbed the wrong power cord and connected it to a 12v source which fried the monitor that only wanted 5V. My Bad. Luckily I was able to get just the sensor and didn't have to buy a bunch of new sensors at the same time.
Replacement parts: If you bought your TPMS from a dealer that specializes in the RV market and attends RV shows then you should be able to get individual parts with little problem. If on the other hand, you purchased mail order from Amazon or eBay or similar, I have no idea what parts or service you can expect.
Testing: This is something I doubt any have done but after some consideration, I think I have an easy and workable plan.
I suggest at least once every 6 months when you are at a location where you have nice weather and a bit of time you conduct an operation test.
With the system on, I would record all the readings from for both pressure and temperature. With the Co-Pilot in the driver seat, I would go to each tire position and unscrew the sensor. The Co-Pilot should signal the tester as soon as a warning is given on the monitor. You might use your phone or walkie-talkie or maybe a 3rd person, as honking the horn as a signal might become bothersome for your neighbors. If all the sensors give a warning within a few seconds (read your manual on the claimed warning time) all is OK. If there is a delay or no warning after say 10 seconds then there may be a problem in either the sensor or monitor or programming and you MUST learn the why and take corrective action as you are depending on receiving prompt warning of air loss.
You can also use this opportunity to confirm your cold tire pressure with your calibrated hand gauge. (See THIS post on how to confirm your gauge is sufficiently accurate) and you can also "top-off your cold pressure with your normal margin of air.