Simple enough, it gets the AC voltage across the sense resistor, around 0.9VAC or so, and this is passed via C27 to a simple voltage multiplier comprised of D19,20 and C25,26,27 so that a DC voltage roughly proportional to filament current is present across R35. U8A and D26 does some gain and clips it so that you only get a DC voltage applied to the filament monitoring pin which is clipped so it will be 5V if the current is ok and 0V if not.
At a guess you should first change C26,27 with new ones, as these are likely getting elderly, and low value electrolytics are always suspect. As well you can monitor U8 pin 1 and it will show you an analogue value that should be reasonably steady at around 4-8V, with no noise showing.
Of course you have checked for dry joints on the filament connectors and that the wiring and interconnects are all fine, and no dry joints on the sense resistor.