I would guess that it's the loading belt that's the problem. They get old and brittle and slip. Not to mention that the pulleys get a bit dirty after some time and need to be cleaned.
Here's the part # for the loading belt for a D70x series player http://parts.pioneerelectronics.com/part.asp?productNum=VEB1184
I'm not 100% sure that it's the same belt used in the D50x series players. But if I had to guess I'd guess that it's the same. (I haven't cracked open a D501 yet, just a D701, D703, CLD-59, DVL-91, DVL-909, DVL-700, & HLD-X9) You might want to call Pioneer to make sure it's the right part number.