How are your DIY soldering skills?
There are full details of how to repair the existing power supply on the reference I gave you. My preference now is to replace the internal power supply with external 12v DC supply and a 12v-5v module inside the TC to supply the 3A or so required for the main board and hard disk.
Even easier if you remove the hard disk completely because then it only needs 5v supply.. all the info and pinouts are there on the website.
You can order a replacement power supply. Tons on eBay.. just type Time Capsule power supply into the search.
They all come from China and most will be refurbished but just as bad as the original. I am not sure what you are paying for them in Israel but most places in the world I would just order another Gen3 or Gen4. They are faster, run cooler and wireless performance is much better. And apple used a different power supply in the later ones.. far superior design. You cannot buy them second hand to use in earlier models unfortunately.
Or buy the Gen4 or Gen5 Airport Extreme which are much better than the Time Capsule in terms of lifespan. Since they use external power supply they don't overheat internally as the TC are renowned for doing.
is there another way to prevent it from disconnecting permanently every time the power is off?
Just use UPS. All network equipment should be on UPS when you have poor power reliability.
Even better use DC .. I have instructions for DIY DC UPS run from SLA battery. (Nowadays you could use Lithium but much harder to charge).
https://sites.google.com/site/lapastenague/diy-ups-dc-controller
This was designed to work specifically with a Time Capsule in situation of bad power where long periods need to be sustained on battery power alone.
Be careful because 12v into the hard drive is very accurate.. you should not exceed 13.2v.. (12v for hard drive must be within+10% and -5%) most SLA batteries are set to 14v and this is really too high for hard disk.. although it might be ok with some older drives.. you are risking it. I did use 13.5v for a while and accepted the risk.. it was OK. But note that a spike would have easily killed the drive and you have no allowance for any overhead.
A different but better way to fix things would be to buy a 1 or 2TB laptop SATA drive and plug that into the TC in place of the 3.5" desktop type drive.. the smaller drives use 5v only and with the board being 5v as well you only need a single 5v external power supply or even better use a 5A 5v module inside the TC so you can supply it with any DC voltage from 9-24v.. and you can then use a float charge SLA battery without any fears of things going wrong.
Btw how bad is it if I'll pull the plug from the new A1355 about every three days?
Remember your NEW A1355 is at least 10years and up to 12years old. Your A1302 is 12-14years old.
When you pull power make sure the hard disk in the TC is not spinning.. just hold it for a few seconds and if you feel vibration wait until it stops.
You will stress it a bit ... obviously just the heating and cooling is not good for electronic equipment. However it is unlikely to cause any great harm. Power on is hard on the power supply though.. so remember that.. and replacements of the original Gen3 supply are very rare.. you would be forced to use DC external supply as replacement.