Motor shuts off after a 45 min ride

I have an 84 SN and I was having a somewhat similar problem recently. It turned out to be gunk in the fuel pick up tube in the tank. I pulled the tube, spray carb cleaner throught and it came out brown. Took it apart and the cone screen in the tube had a bunch of crap stuck in it.
Relative easy and worth a shot.

Could be ballast resistor. Classic symptom...

Best way to test is next time the engine quits, be prepared (with onboard tools) to move all wires (at the ballast resistor) to one of the two terminals. If the engine then starts and runs fine, you leave it this way for the rest of the outing, but be sure to change it out before the next outing to avoid burning the points or module.

Did you install the HEI ignition before or after this problem started to occur? If before, is there any change at all with the occurance of this problem? With the HEI you should have gotten rid of the ballast that David F mentioned. However, he does suggest testing for spark when you have this problem which is exactly what you should do. Be ready for when the engine acts up,...when it quits completely disconnect one of your plug wires and insert a small bolt or something into the plug end boot. Fix this end so that it's about 1 inch away from ground. HEI systems are very strong and should have no problem at all firing across this gap. Crank the engine over and you should get spark accompanied by a very audible snapping sound. If not, start looking at your ignition again. If the distributor is known good, follow the ignition wire to the distributor back from the switch and see if it has good continutiy. Check the terminals on your ignition switch. Over time the wires vibrate and copper strands start to brake. Before you know it wires are just hanging on with a single stand. If you get to this point and everything looks good, write back and we'll go from there.

Thanks everyone for the replies. The problem that I'm having is exactly the same as before the change to the HEI setup. And I don't have a ballast resistor anymore. The HEI came with a new coil. Could the timing affect something like this? The way that it just dies doesn't seem to be timing related. It definitely seems like like a heat issue within the engine cover area. It would probably be a good idea to clean out the pickup tube in the tank, but the problem seems to be too consistent like clockwork. Checking for spark next time is a good idea. Maybe I could use a timing light to check for spark? It may be a while before I get back to the lake as it is an hour from my house. The boat is in my basement where I can work on it at least. I hope that the above answers some questions and please keep the feeback and theories coming. Thanks Again everyone.

I would say no to your choke idea. The heat does the exact opposite to the choke, it opens it.

My choke is the electic choke and the heat rise is not connected. Some of the choke parts are actually missing. The electical parts are there along with a connecting rod and the plate. I never use the choke, I may remove it anyway for better airflow. One less thing to go wrong.   

I have removed the 90 deg fitting from the tank and the tube is still at the bottom of the hole. Maybe I can unbolt the sending unit, reach in, and push the tube up from inside the tank?

I did some work on the boat and it seems to run without shutting down. The pickup tube in the tank was actually welded in (aluminum tank). I removed the float and reached to find this. The piecs in the top of that tube is some sort of creen or something that I couldn't see or remove. I sprayed carb cleaner in the tube about 20 times to clean the gunk out. Yeah I know it went into the fuel, but at least the tube is clean. I also cleaned the fittings and replaced the fuel line from the tank to the pump. I also replaced the fuel filter and removed the choke plate as I rarely use the choke. Now it runs without breaking down. Hopefully it will become a reliable boat and not break down every time I go to the lake.