Hi...
I had one of these types of seat posts on a hybrid bike some time ago. At the time it seemed ok, now for road riding I can't imagine using one.
Hmmm, if you weren't having problems with the seat before on the old bike, but now are with a new bike and suspension post...then it sure sounds like the post isnt working out for you.
Another possibility is just that the bike fit is not ideal. That can cause a lot of problems. You said the seat starts ok then slides down, so I dont know if that's a problem with the post or inherent in the design.
Maybe try the new bike without the suspension seat post. It would be a good place to start.