2007 Mitsubishi Galant Air not cooling stongly & noise

Recently, I have had the air in my car progressively getting warmer. After several days of this behavior, the AC light started blinking(according to the book, needing to be checked out). When I took to car shop, they said the freon was low and recharged the system and put in a dye to detect any leaks. That worked for about 3 weeks, but then the same problem came up again. They checked out the car and said they only saw a slight amount of dye on one of the valves and replaced that and the freon for only $10(as it had been less than a month since the last repair). Now, 2 weeks later, it is starting again. I notice when I am sitting at lights or with the car in park, it sounds as if the AC system keeps turning on and off every few seconds(the type of sound you would normally hear when you first turn on the AC, but mine then cuts off, then on, then off again). The shop said they would just replace the line, but I wanted to see if it could be something else(fix the problem all at once): could it be a compressor, line blockage, something else? Thanks for your help!