Time machine fails to complete/maintain a backup

Question

Time machine is driving me nuts!:
The last successful backup was one month ago.  Since that time it seems to have been stuck in a perpetual loop of trying but never successfully completing a backup, no matter what I try.  Here is the history:
I bought a new iMac 6 months ago with OS X Lion (1Gb HDD).  Set up Time Machine over wireless network with a 1Gb WD MyBookLive attached to a new BT Homehub 3 router (UK).  Lion successfully backed up my system (total size approximately 159Gb) over a two day period, but every 4-6 weeks Time Machine would tell me it needed to create a new backup. Frustratingly, this meant that the backup history never stretched very far in the Time machine 'starfield window' but at least I had a backup of some sort.
I upgraded to Mountain Lion 3 months ago, in the hope that it would fix the error and, briefly, things were going well.  Time Machine didn't need to create a new backup from scratch after upgrade, and continued to add to the existing backups & history for 2 months.  Then i got the dreaded 'Time Machine needs to create a new backup' message and, 1 month later, it hasn't been able to finish the process yet!
After about 6 days it was about 30% complete (just over 50Gb) which didn't sound right given how long it previously took.  I stopped the backup using the TM dialog box , reset my mac, router and MyBookLive and started again.  Time machine automatically started again, and after several days of crawling I got the message that the 'sparsebundle was already in use'.  I followed the suggested tips regarding unmounting the drive, reset everything and tried again.  TimeMachine took about another 4 days to get to about 30Gb, then stopped itself with the message that the backup had failed.   I tried deleting the preferences files for TM as several sources suggest, but this doesn't seem to have helped, TM just takes days to crawl along and then terminates saying either simply that the 'backup has failed' or that the sparsebundle is already in use.  About 5 days ago I used the WD browser-based administration tools to create a new, separate, share for TM (presumably because this ensures that there can be no record of any previous backups on the backup device which TM sees) and set up TM from scratch.  All seemed well, it took only 23 hours to back up 103Gb - then it failed, saying that the 'sparsebundle is already in use'.  I set the backup away again overnight and it managed about 12Gb before the same message appeared.  TM now estimates 5 days to backup the remaining 40Gb.
Somebody please tell me what is going wrong and how to get TM to actually complete a full backup then maintain it without constant intervention!!!
Some further points worth mentioning: 
1) My iMac is located too far from my router to backup using ethernet cable.
2) I have used iStumbler to determine that the signal strength is 36% (surely strong enough?) with only 3% noise. (802.11n Gigabit Ethernet). 
3) WD MyBookLive plugged into the GigE port on the router, and firmware is up to date.
4) I've searched Pondini's tips, from start to finish looking for a solution, as well as the Western Digital and BT forums, but none of the common solutions seem to work.
Help! and thanks.

Answer 1

Thanks, Linc, for your response.  I will also seek advice from the manufacturers of the other devices, however, I fear that every party will foot the blame at the door of others. 
I don't agree with your suggestion that this shouldn't be my only backup, given the marketing literature of both Apple and Western Digital.  Apple state on their website: 
"Connect the drive, assign it to Time Machine, and start enjoying some peace of mind. Time Machine automatically backs up your entire Mac, including system files, applications, accounts, preferences, music, photos, movies, and documents."
Similarly, Western Digital state about their MyBook Live:
"Mac users can utilize all the features of Apple Time Machine backup software to protect their data."
So where, I wonder, does the fault lie?  At the end of the day I am a home user and 'consumer' - just your average Joe looking for a robust home computing solution, not an IT boffin with an in-depth understanding of the nuts and bolts.  I expect both products to do what they say on the box.  Not surprisingly BT (the supplier of the router) state "The wireless 'N' technology in the BT Home Hub ensures you get a more reliable wireless connection throughout your home at all times."
To me, the advantage with my set up (should it ever work) is that, should the unthinkable happen and my computer is stolen, the likelihood of my backup device disappearing with it (as might be the case with a locally attached device)  is greatly reduced because the NAS is hidden away elsewhere.