Some reading for you relating to your issue:-
1/ link
2/ link

If you are handy with tools and confident you can probably fix it yourself but it's probably not a job for the feint hearted. Never the less it does appear to be a common problem (though I admit not having come across it before) and can clearly be fixed. If it's not a job you wish to attempt yourself then some kind soul on this forum may I feel sure be able to point you to a Pentax repair shop.

Good luck.

In what way isn't it working?

A nice purchase and I'm sure you won't be disappointed.

I recently picked up a mint condition SMC Takumar version of the 24mm f3.5. Identical optical construction I believe to the K 24mm f3.5 and I can confirm it to be a little gem of a lens. Actually it's not that small in size being quite a bit chunkier than the 50mm Takumar for example. Mine came with genuine Pentax caps and case and also a genuine dedicated square lens hood within its own dedicated square Pentax case. I won't upset you by telling you how little I paid for it but the square hood alone (if you can find one) I've seen for sale at two to three times what I paid for the set..

Anyway, I'm sure you will find it to be a keeper lens so enjoy it.

Plus 1 to all of the above.

'Tis amazing what one can learn from photography.

Highly recommended viewing for all photophiles:- link

A worthwhile watch which I hope you enjoy.

It does rather sound like a failing capacitor which as Lubbyman says above is also an issue with the Q.
The key to avoiding time & date reset is as suggested above again by Lubbyman but I would further add, don't wait until the K20d battery is totally drained and equally important, before swapping the battery, switch the camera on and leave it switched for at least 5mins, preferably a little more, (you may need to experiment) in order to charge up the capacitor. At this point do a rapid battery change. This method works every time for me with my Q.

Good luck.

For the ardent collector - only £3600.00 but you get free postage

link

I'm not saying it's a good deal!

Lovely set. Colourful and cheerful. Love number nine with its painterly background.

Very nice images indeed. I visited Durham Cathedral just a few weeks ago and a beautiful place it is too. I found it quite dark inside and a challenge to photograph. Looks like you had no such problem though. Congratulations.