I had a similar problem with my ProSine 2.0 and decided to open it up to figure out what was going on...
I discovered that one of the circuit boards had come un-seated from it's edge connector on the main board. I re-connected it, but it un-seated again just a few months later. I ended up machining a couple of U-shaped ABS plastic clips to mechanically hold the connectors together. See photos below. It's been a few years and the inverter is still going strong.
I also have (one) EU2000i and use my ProSine to start the A/C... haven't had any issues with the transfer relay as far as I can tell.
And one last thing; I installed a single 20A outlet on the front panel of my ProSine and wired a power cord into the Prosine's AC input leads and put a 20A Edison plug on the other end. In the event the inverter ever fails I can simply remove it from the circuit and "plug" my shore power back into the main breaker panel that is usually fed by the ProSine.
Hope this helps.
Cheers
-Mark