Do the individual pieces of your parquet floor fall out?

I live in an apartment that has a parquet floor with this pattern:

http://www.woodfloordoctor.com/_product_reviews/articles/img/parquet3.jpg

The individual strips of wood keep coming up when I walk on them – in some places they are not longer glued to the floor. I want to find some really strong glue to fix these individual pieces (about 30 here & there). In the spots where they come up, both the back of the piece and the floor is rough with the residue of the original cement/glue so the new glue will have to be pretty strong in order to combat this. If you’ve had this same problem can you tell me how you fixed it?