hair dye fades within a week after bleaching

Permanents have bleach in them, to lift out your natural colour and deposit replacement colour.  Blondes usually have a bit more peroxide in them than normal colours, as well.

So you have effectively bleached your hair three times in three weeks--it sounds really damaged.  Damaged hair simply will not hold colour.  How is your hair's condition?  Is it gummy/stringy/stretchy when wet?  Dry and frizzy?  Snapping?

Avoid the ash blonde permanent dyes--instead, get some ash blonde toners and some silver or violet toning shampoos, which won't damage your hair.  Reconstruct (With Joico K-Pak) and deep condition (With Joico Intense Hydrator if you can afford it, Aussie 3 min miracles if not).  Don't wash every day, and avoid heat styling if you can.

http://www.hairdyeforum.com/index.php?topic=1935 <--- this thread has great advice on how to repair damaged hair and how to treat it until it's feeling in much better condition.

Agreed.

Concentrate on condition rather than colour at the moment. Once your hair is repaired it should hold colour better.

Yep, sounds like the hair shaft has become so porous the colour is just washing straight out/off.