Are you saying that once you back off the throttle the transmission remains in 2nd gear? Or are you saying that with the throttle open wide it won't upshift? Or are you saying something else? I'd start with a basic look at the kick down cable--sticking? frayed? adjustment?(may need to be loosened) and the shift linkage for worn bushings. The BW35 is not a very sophisticated auto -- it takes a very open throttle to prompt a kick down -- then you get a lot of sound and fury and some increase in forward progress. Like old Fordomatics it has a neat feature in that it will hold 2nd gear (obviously not something you'd be thrilled about right now) by starting in L - manually shift to D to catch 2nd and then before it goes to 3rd put the shifter back in L -- it will hold 2nd for descents -- shift back to D for 3rd.
There's a centrifugal governor in the tailhousing -- easy to access with the transmission in the car -- they can/do stick. If you get involved taking down the valve body to check for sticking be sure to have a spotter to see where the odd spring or check ball goes to. Been a very long time since dealing with one. And type "F" fluid. -- Dave