Missing files after a transfer to a mapped drive

I have a weird problem. Here are the specs:
Computer A - Intel Quad Core 2.4GHz - Win 7 64bit
Computer B - Intel Pentium 4 3.2GHz - Win 7 32bit - Shared drive - no password.
Network - gigabit wired
Same workgroup on both computers.

Mapped the drive from computer B on computer A as Z:drive
When transfering let's say 20 files (let's say mp3's) from computer A to Z:drive (computer B) it only transfers about 4-5 files. At this time if I refresh the folder containing the 4-5 files on the mapped drive it will eventually show two more files.
If I select all 20 files again and try to transfer them to the same location, it will prompt my that some files are already there. After clicking on "do not copy", it will copy another 6-7 files to the shared drive. after a refresh to the folder (on shared drive) there are 2-3 more files.

I can't seem to figure out why this is happening. I tried from another computer (win 7 64bit) via wireless and it never does that (to the same mapped drive).

Any suggestions?
 
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