I've tried to do as much research as I could about this topic but I am still scratching my head on this one.
Its not the biggest deal to just clear some codes before you drive, but it is annoying and I would like to use the key fob.

Some history:
I bought my 1999 C5 three years ago with less than 30k miles, it has a K&N air filter, Borla exhaust, and stainless steel headers (not sure the manufacturer), but it runs and sounds beautifully.
One year ago I had to replace the slave cylinder when the clutch hit the floor and wouldn't return.

Two years ago I took it into the shop and got 4 new Continental Run Flat tires, and since then both rear TPM sensors do not display pressures in the DIC.
The tire sizes are standard for the C5 and were put on the stock 1999 rims.
I did not follow up with the shop about it because I did not trust they would treat my C5 with the love it deserves.
I saw on another post (That I cant find for the life of me) that they were having TPM issues with what I assume to be a similar tire because they said run flats and max PSI of 51. (I run 30 PSI)
This made me think that maybe there was an issue with the design of the tire if the two wider rear tires are not reading and the fronts are working fine.
But in that post the user wanted to delete their TPM system, for now I'd like to just fix the issue, might delete later though but I am undecided.

The previous owner stated that the key fob just needed a new battery but worked.
According to the Carfax, he took it to the dealer and bought 4 replacement keyfobs, one every year for 4 years, so I assume this isn't just a battery.
It was marked as "Anti-theft/keyless remote(s) replaced"

The codes in the DIC are:
C2110 Right Rear TPM Sensor Malfunction
C2115 Left Rear TPM Sensor Malfunction
***No RFA NO COMM code

Some steps I have taken so far:
Fuse 27 (HVACCOM I think) checked with multimeter, all good.
Attempted Key Fob learning in DIC with no luck no matter how long I held the buttons down.
Poorly attempted to test if Key Fob is functional with a multimeter, I only know it is getting power to several points around the board.
Attempted TPM learning in DIC using a circular magnet, only the front wheels registered.
Check power to RFA unit above driver rear wheel and got 12 Volts on the Orange and pink wires. (Not sure how to check the ground connection, but this should be ok because the front wheels work, right?)
Battery charged and tires off right now, I'm doing a brake and rotor job and figured I may as well fix this too.

Next Steps:
Going to take the Fob to AutoZone to use their fob tester, if it works, I'm not sure where to go from there.
If the fob doesn't work, then I assume that the sensors in each tire are either missing, have dead batteries, or simply don't work well with these tires.
If that is the case, I will wait to get new sensors when I get new rims and tires down the road and just get a new key fob.

The Fob does work.

Does anyone have an idea of what could cause a key fob and two TPM sensors not to work while the RFA module receives power and registers the front tires?

 

Perhaps the batteries in your rear TPMS sensors are dead.

 

My problem was similar but not the same. I had TPMS errors and my remote wouldn't sync.

I recently replaced the receiver (it is on the driver's is side under the hatch behind the plastic trim.

Fixed everything.... mine is a 2000.

 

Thank you everyone for your help.

I bought a GM TPM relearn tool, going to see if the batteries are dead in the rear tires today.

I just don't think the RFA module is bad because it learns the front tires and has all the power it needs, but if the TPM sensors have power I may change it out like you said.

 

If it doesn't fix it, mine still picked up the TPMS, just didn't work with the remote. Got a new remote, didn't work. Got a new receiver and that fixed my problem.