Time Machine no longer functions for me

My wife and I, using our separate computers, have been using TM successfully for years through various OS versions up to 10.6.8. Now, over the past couple of months, but only in my case, it is become completely non-functional. Although our sparsebundles are where they always were (and, BTW, my wife backs up using TM to the same disk partition with no problems) TM will not incrementally back up to mine but, if anything, tries to back my complete disk contents. But invariably it hangs up in the middle, then loses the identity of the backup disk, and never finishes. I changed the disk and it did the same, got hung up, wouldn't complete a backup and eventually stated that the backup disk couldn't be found.

When I again reset the backup disk to the new empty partition, I got a message saying that TM couln't access the backup disk (Error OSS2).

I have plenty of space available on each partition (2TB divided by 3). It also ocurs whether using wifi, or ethernet.

Since my wife's backups are proceeding normally, it doesn't seem that there is a problem with the disks and the network.

If it's a software issue, what should I do?