From the prints, it looks like you've got 5.6 volts present on ELT. I don't know if this is a charging voltage (if there is one) coming from the aircraft or if it starts at ELT.
I would think the aircraft is providing it.
Also..... without having access to the manuals, this might be a low ELT battery indication.
You’ve covered all the bases on the wiring checks.
Reading 429 data bus wires requires an adapter.
The RTX adapter was the cheapest I could find. It is a single channel “receive” only. Numerous manufacturers have their own software and adapters.
These usually have multiple transmit and receive channels. They’re not cheap. My RTX was about $800US.
I would see if one of the user units has a bad 429 receiver (which I've seen before) which is locking up the entire data bus.
Disconnect one to see if the other two come up. If not, hook the first one back up and try another. Try it again on the last unit.
Is either of those data bus wires shorted to shield or ground??
Do any displays show annunciation or range marks that would indicate the data "is" reaching the display, but not the actual weather? If that was the case then you would need to go back upstream to the antenna input.
It looks like you've got a jumper that tells the unit to send the output to EFIS, is that present?
If things are working fine for 10 minutes and then not..... it sure sounds like a component is heating up and then failing. I'b bet it is the indicator.