A flat a week is a lot. I've been biking seriously since right around new years' and I just got my first flat last week after logging about 550 miles flat-free. It was from a little shard of steel tire belting wire (see
this for an example of the source of such road debris) that poked through the casing and tube like a hypodermic needle.
When you are getting all of these flats, are you certain that you've found the real culprit each time before moving on? I always mount my tires so the tire's label is aligned with the valve stem. When I get a flat, I open it up and find the hole in the tube. Because I know how the tire sits rotationally against the tube, I can find exactly where in the tire the pincture should have come from. With the flat I described above, I looked at the corresponding spot on the tire and found the little piece of wire hanging out of the casing ready to poke my tube again if I didn't remove it.
If the puncture is on the tire side of the tube, look until you find what caused it and get it out of your tire or it will give you another flat in short order. If the puncture is on the rim side of the tube, you need to inspect your rim for burrs, nicks, scratches, etc. that correspond with the location of the puncture. Also inspect your rim tape to make sure it is still intact and properly covering the spoke nipples or holes and that no burrs or spoke tips have poked through the tape. Not using rim tape? get some! It only costs a few dollars per wheel and is technically reusable several times if you are careful. Rubber rim strips are garbage and do not work well at all with higher pressure tires in my experiences.
I keep hearing that armadillos have poor handling in inclement weather. Are they too plasticy to grab the pavement well, or what? Nobody ever explains what the problem or even symptoms are other than vaguely stating that they handle poorly. I'm just curious.