My primary suspicion is Q8, it takes 56v and through a 330 ohm resistor turns it into 35v, which runs the protection circuit, including the relay.
Q8 is an itty bitty to-92 package, a to-126 package would be a lot better. It can dissipate 1.2 watts when bare and 10 watts heatsunk.
This is the same mod as the infamous Q5 & Q7 on the sx-950.
use a
512-KSC2690AYS to-126 ecb 120/a160 1.2a 20w 155mhz 35-320hfe $0.40
or
512-KSC2682YSTU to-126 ecb 180v .1a 1.2/8w 200mhz 100-320hfe $0.31 ea
I had been recommending the 2682, as the circuit wouldn't pull over 100mA, but the 2690 doesn't seem to sacrifice anything, and can handle more current. Plus the 126 case has no exposed metal that could short, thus any added heat sink would be electrically cold, unlike a to-220 case.
If you want to go nuts, you could get either:
512-KSA940TU_Q pnp to-220 bce 150v 1.5a 25w 4mhz 40-140hfe $0.54
512-KSC2073TU npn to-220 bce 150v 1.5a 25w 4mhz 40-140hfe $0.54
or go whole hawg and use:
863-MJE15033G pnp to-220 bce 250v 8a 50w 30mhz hfe:70 $0.87
863-MJE15032G npn to-220 bce 250v 8a 50w 30mhz hfe:70 $0.87
in place of the d313's (Q1,Q7:npn) and the b507(Q4
np) on the heatsink aready.
I would worry slightly about the 1/4 watt series resistors R11,R12 & R21 at 10 ohms and R20 at 3.3 ohms, because if they were abused they just might have been made intermittent instead of popping outright, like a fuse.
But I would expect that just a Q8 replacement is warranted.