It would probably help if you could post a picture of the situation.
Is the sill piece a 2x4 or 2x6 board?
If so, perhaps after you remove existing and clean up the area
you could slip in a new piece of treated lumber of similar size or better
yet slightly thinner.
You would want to use a lot of polyurethane caulk/adhesive.
Goop it on to the slab and the top of the new board and slide
it under the bottom track of the slider. Step on slider track to
make good contact.
You could probably secure all the way through the board into the
concrete by drilling with hammer drill (rent one if necessary) with 3/16?
bit and securing with those flat head blue concrete screws.... Just be
sure that they won't be in an an area that will interfere with rollers.
Just some guessing ideas at this point. A picture would help.
Good luck!
RC/DG