First of all, the short amount of driving you do prior to getting them refilled is not going to cause the tire itself any problems. The biggest problem you'll see with tires which are run low is the amount of heat build-up in the rubber. Not only is the low pressure not really that low, the distance you drive is not enough to cause you worry.
Secondly, I'd suggest you have a slow leak (obviously). There are only two places where you can have a slow leak, discounting an outright hole in the tire.
The first place is the valve stem. If these were not replaced the last time tires were installed (except for Tire Pressure Monitoring Systems - TPMS), the shop did you a disservice. New ones should be placed each time to ensure there aren't any problems for the life of the tire. These could possibly leak through the valve core (schraeder portion) or where they seal to the rim. TPMS valve stems could possible have issues, but are usually more robust than regular normal ones. These are much more expensive to replace.
The second place is where the tire seats on the rim. If this area was not cleaned correctly, has corrosion, a leak could form there. If lube/sealant (many tire shops here in the states use soapy water) was not used during the installation process, this could also lead to a leak.
As for the leak itself, I'd suggest your tires are leaking at the rim. Something a lot of people don't realize is that the act of driving helps to keep the tires sealed on the rim. When the tire is ran down the road, there is a certain amount of heat build-up (as I already suggested) in the tires. This softens the rubber just a little bit and allows it to become more fluid (for a lack of a better word). This fluidity means that the tire is pliable and will move where needed to flow around the rim and remain round. Mind you, this isn't big amount. Just enough to help keep the tire sealed on the rim. When a vehicle sits for a longer period of time, the tire starts to incur a flat spot. This flat spot also transfers to where the rim meets the bead of the tire. Very small gaps can occur at these spots, which can cause the small air leak. Again, these are not large gaps, be enough for air to escape. Another thing to think about is that as a tire has less and less air pressure in it, it has a propensity to leak faster. So, your tires may leak down 5psi each week (if left alone for a long length of time) until it gets to say 15psi, then drop down to nothing by the next week. (This is an exaggeration to make the point). Just by keeping the pressure up in the tires, you'll shouldn't run into this problem.
Bottom line here is, you can do two things:
- First, drive the car more. In my opinion, this is where the main problem lies. This also helps against dry rot cracks forming.
- Second, you can possibly take it to a tire shop and have the tires reseated (break the bead, throw some soapy water sealant around the rim, and reseal the tires). This would probably incur the cost of the reseat, plus the added bonus of having to have them rebalanced.
