I have seen this type of thing countless times in my 20 years plus in the repair biz. Convergence going out on CRT RPTVs is very common, like a thermostat going out on a car. You just remedy it and keep driving her, it's really just a bump in the road.
If it's still intermittent, you have a chance to fix it without having to put new parts in. If it has gone over the edge to not snapping back in, chances are the parts will need to be replaced. When cold solder joints cause non-connection, the ICs start getting run outside of their design parameters, eventually causing them to overheat and/or simply die. They could also short, causing the power supplies feeding them to be compromised. I have seen this happen, where the set actually shuts down permanently after a certain point, because the power supply that runs the +24v to the ICs has been shorted, and that's what allows the set to turn on. Without it, it just stays in shutdown.
So don't dally once your set has gone intermittent! It could get worse. Get it fixed ASAP.
If your intermittency is still alive, resoldering your ICs - which get ungodly hot in there - will usually restore everything without further ado.
It's a pain getting in to do that resoldering, tho, and that's where all the time and energy of this fix goes.
All HDready Mits have a light box that is removable from the main box, for spiriting down to the shop. It involves removing 4 screws on each side - 2 big bolts on the floor and 2 flatheads at CRT lens level per side, all screws/bolts #2 Philips head - plus disco'ing the wiring to the front of the set. This is much easier and much safer than disco'ing all the wiring needed to get a board out, and taking a board out, where you might inadvertently mess something up when you put everything back together.
Once removed from the main set box, the light box can then be up-ended to reveal the legs of where the ICs are soldered in. The resoldering itself is very straightforward and only takes a few minutes. As already mentioned, just adding a bit of solder to each leg is all that is needed.
If you need to replace the ICs, be sure and be liberal on the heat sink compound, as it is critical for heat transfer away from those ICs to the heat sinks themselves.
But replacing a board when there is a convergence problem is never the best solution. Starting out from scratch on your geometry and convergence is something that requires lots of time and experience just to master, let alone accomplish with finesse. And is not needed when you simply repair the board in question - as in resoldering or replacing ICs, rather than replacing the entire board.
PS - your convergence paradigm in there might be overheating the ICs. I have seen some really dorky work done on the convergence at the Mit factory, with lots of registers fighting each other.
This can all be straightened out, and I do so whenever I encounter it, as part of my basic calibration package. Just like optics cleaning, which is another absolutely essential part of that package. I encountered one Mit HDready where all the numbers in the point system were positive, and in the hundreds, whereas they SHOULD all revolve around an average of zero, plus or minus. When I zeroed them all out to start over, the picture had shifted itself to the side by 7"!
So if you have me calibrate your set and it has these registers fighting each other in there and causing excessive heat by so doing, that sloppiness on the part of the factory gets cured in the process.