Things to check:
- when the a/c stops blowing cold, does the compressor still run? (you say you don't hear it cycle, but you didn't answer the question of is it running? If not you have one of the following: Bad A/C clutch coil, bad relay(you already replaced that you said), bad high pressure switch (or it's working and you have high pressure), bad low pressure/cycling switch (or you are under charged or have other issues), bad wire(s) (power feed).
- Ever have the a/c worked on - if so what was done?
If the system was opened and a good vacuum not drawn (30+ min down to less than 1000 microns of vacuum) there could be moisture in the system. Moisture will freeze at the expansion orifice and stop cooling.
Did you or anyone ever add sealant (very very bad!!!) This causes all sorts of issues and will void any warranty. There are 2 types of sealant - moisture/air activated (very very very very very very bad) and seal swellers (very very bad). These void any and all warranties from anyone. I check for them before I work on a system and will not touch it if found and I label the vehicle that it has sealers in it.
Does this happen when driving, sitting, both, etc?
If you have high pressures have you checked your fan clutch?
If you had it worked on, does it have R-134a? Most shops don't have a refrigerant identifier (infra-red spectrometer) and will such crap from one vehicle and spread it to all others (just like they do sealants). All sorts of stuff can happen if the system doesn't have the right refrigerant.
Did someone overcharge the system with oil? These only take a few oz of oil.
Also - FYI - a low charge will not properly circulate the oil and will starve your compressor - want to save your compressor? - don't let your system run a long time with a low charge. Of course a overcharge will over tax the compressor.
When hooking up gauges, just turn the knob on the valve until you see pressure on the gauge - then turn a LITTLE farther. I've seen where folks hook up their gauges, crank down the valve all the way and bend the schrader valve. Some can be replaced on the vehicle (with the right tool), some need the refrigerant removed, some need the hose replaced. Just a warning for you.
A professional mechanic trained in A/C repair with the right tools can help you. However, most don't have training, have minimal tools, and don't have a clue what they are doing. (sorry - had to rant a little - it just ticks me off when I see people getting screwed by these types).