"I have trouble starting my rider after it sits a while. If I put my
10A charger on it for some 10 minutes, the mower starts fine.
I find no evidence of a drain on the battery. "

Did you put an amp meter on it and measure the drain with the mower
turned off? How long is awhile? With the mower off, the drain should
be zero.

"The battery is relatively new, one year. I replaced earlier battery
with same problem. "

What happens if you fully charge the battery with the charger, then let
it sit unused? If it goes dead then in a short time, either there is a
drain coming from a short somewhere or else it's a bad battery. You
can rule out the short with an amp meter.

You should get a battery tender and keep it on the battery for the
winter. If you do that, you can get many years out of a battery. If
it sits and is allowed to discharge over the winter, that is the kiss
of death.