Time Machine quits when I try access a backup

I had a Time Machine (TM) backup extending back many months, and yesterday I had occasion to use Time Machine (TM) for the first time in several weeks.

When I selected the week that I wanted to return to using the right-hand "scale" of backups, TM immediately quit and took me back to my current desk-top. I tried again, using the "back arrow", with the same result - TM quit and I went back to the desktop.

What I've tried so far, all without solving the problem:

1 straightforward restart

2 restart in S mode, and running /sbin/fsck -fy

3 Pondini's troubleshooting steps A4 and A5 (full reset of TM and Repaiing TM disk)

4 starting over - erasing the TM disk and creating a new TM backup

My TM backup is on an external Lacie drive which is connected to my iMac directly via FW. I am using OSX 10.7.5

To restate the issue: TM makes backs up, but quits immediately when I try to access one.

Can anyone help?