Firstly, when you get a flat, you should make a mark across the tire and rim, and also remember the left-right orientation of the tube. Later, you can use this mark to align the tire to the rim exactly as it was when you got the flat, and from the location of the leak on the tube, you can later find the exact area of the tire and rim corresponding to the tube leak. You can focus your search for the problem there. Sometimes foreign objects are embedded in the tire such that they protrude very little and are not palpable. I have seen a bit of glass do this, as well as a piece of steel staple: basically sitting flush with the tire both inside and outside.
Pay attention whether these punctures are on the outside of the tube, where the tire tread meets the road, next to the sidewall or inside of the rim. That's a clue. A foreign object from the road won't ever puncture the inside; that suggests a rim problem.
Punctures are caused by foreign objects, by pinch flats, and by sharp edges in a rim. Pinch flats are due insufficient tire pressure allowing the tube to get pinched between the rim and some object that you hit while riding. In cheap, single-walled rims, the spoke nuts protrude into the air chamber area and come into contact with the tube. They also exhibit rough edges, and must be securely covered by a rim tape. Sometimes what passes for rim tape on cheaper bicycle wheels is just a rubber band that is supposed to stay in place under its own tension.
See this table for a ballpark tire pressure you should be using as a starting point, based on your tire width. If you go significantly lower, you risk those pinch flats.
Also:
... many patches ...
Patches will leak if they aren't done properly; the more of them you have on a tube, the greater the likelihood of a leak. If you have three patches, and two are good, but one is not so good, that's exactly like a tube with a single not-so-good patch. They all have to be excellent. When I patch a tube, I press the patched area between two wooden planks using a pair of F-clamps, and leave it clamped for at least 24 hours. After that I pack it up into a box; I don't use that tube right away, but carry it as a spare. That gives it more time to cure before the first inflation. After all that, I still cross my fingers when using the tube for the first time, and closely monitor the tire pressure in the days that follow.
