I went to the farm today and I THINK that the spayer is now fixed - many thanks for all the help here.
I first spent some time looking it over before hooking it to the tractor; I wanted to look at it and think about all the things you folks told me to check. It is a 6 roller pump, and the line from the tank to the pump is 3/4" and not 1" as I thought. The tank is vented ok.
I took the line between the pump and tank off and retightened the hose to the fittings. The only strainer is in the fitting where the hose attaches to the tank. It had a little debris on it, but wasn't stopped up. I hooked it up to the tractor, put 25 gallons of water in it, and sprayed it out over a field. It held 50 lbs of pressure for about 10 gallons, then dropped to 25, then to nothing. I got off the tractor and checked the main hose, and it was showing signs of collapsing in a couple of places. The pump was obviously sucking hard, but not enough water was coming through the line.
So I checked the strainer, and there was a little debris on it again. It still didn't seem to be enough to cause a problem, but I washed the tank out as best I could. I took the main hose off and reinstalled it so that it was perfectly straight in the hopes that it would have less of a tendency to collapse. Then I decided to check all of the fittings again to see if there could be anything that was letting air into the system. I noticed that the pressure gauge could be turned slightly, so I decided to try to tighten it down. I was afraid I was putting too much pressure on it and was about to break it, but I managed to make a complete turn with it.
I put another 25 gal of water into it and tried again. This time the sprayer worked perfectly. The loose pressure gauge was definitely a problem - instead of bouncing between 40 and 60, it stayed right on 50 and didn't move at all. It stayed there until the tank ran out of water. It came from the factory with this problem; it has always bounced around and I thought it was just normal for it.
I'm not sure what I did that fixed it. Could the loose pressure valve have been the main problem all along? I guess the real test will come in another week or so when I spray with 2-4DB, but I am far more optimistic about it than I was earlier.
Thanks again to all who helped me.