'93 LSS tranny problem

have a 1993 Delta 88 LSS with the 4T60E transmission. It has developed an
unusual problem that I hope someone can explain.

During the first 10 miles or so of driving, when I have to come to a stop,
the transmission will not downshift to the lowest gear. When I come to a
full stop, it acts as if it is in neutral - stepping on the gas just revs
the engine. If I wait a while, say 15-60 seconds, it will usually drop back
into gear and run normally.

I have discovered that, when this happens, if I move the gear selector to
"1" (low gear), it will usually engage right away.

After I've driven 10 or so miles, the problem pretty much goes away. The car
has 135,000 miles and the tranny has had a fluid and filter change every
three years.

Any ideas anyone? Thanks.

I suspect internal problems here, but you could have a trans shop scan it and look for solenoid issues and gear ratio/slippage errors. It will have to do this when they check it though.