Hi John,
is that RevC Multilink a blue one with a attached female header (not flat band cable)?
If so, I used one for years too, and then the connector was causing problems like you describe because of a mechanical stress and connection issues. You might try to resolder the header contacts (heat them up and add some solder).
Other than that: I'm using the P&E Universal Multilink (the green box) with a flat band cable with my 52259 projects, and have not faced the above issue, as the flat band cable solution worked much better in my view for my usage.
Other than that: Freescale sells the USBTAP for ColdFire (BDM), but I only had used it once (tried it out in a trial period), and then switched to the P&E Multilink as smaller and better to use.
Hope this helps.