Why 22k? It seems pretty high to have. Your post suggests you've tried a lower value like 1K; if both PICs are running at the same voltage levels, then altogether do away with the resistor. Due to the resistor, it is possible the logic low level is not being met. If you fix this and still get the problem, then continue below.

I suspect the problem could be the software serial not getting the start bit reliably.

What you can do - since you use the 1936 is to configure the receive pin as interrupt on change pin; I believe all pins have IOC ability on this chip.

When you get the IOC interrupt, invoke the serin2 command in the ISR

I cannot advise with code as I am not up-to-date with PicBasic since some time now.