Hi flyin_sweed...(clevr hndle!)
Sorry she's giving you trouble.
This problem could a sign of a couple of things.
The first, and most alarming, is that your outboard may be overheating. These old girls are meant to run fairly cool. Around 160 to 170 degrees Fahrenheit TOPS. If it is overheating, each time you allow it to get to the point it shuts itself off, a little more damage is incurred and the longevity of the engine is at stake. So, ensuring that overheat is NOT occurring is of the utmost importance. As it approaches the temperatures I just listed, if the temp continues to climb, you must be prepared to shut it down before it gets much higher and figure out why. If the pee stream is strong, then it is likely a thermostat issue. Or. it could be a buildup of deposits in the coolant passages. Sometimes a flush of pressurized water BACKWARDS through the head and engine block can do wonders. Many people use vinegar or a product called "Salt Away" to aid in the process. Of course, this is done with the thermostat removed to gain access to the passages so it is an opportunity to re gasket and replace the stat. The use of compressed air AND water can work well when "backflushing" too.
Also, I don't recommend running an outboard in a closed container for more than 2 or 3 minutes at a time unless there is a steady resupply of fresh, cool water constantly flowing to keep the engine cool.
If you find the engine is cooling properly but still shuts off after a time, try running it wth the cover removed to see if that makes a difference. If that has positive results, then it's likely the engine has an exhaust leak and is "choking" itself out under the cover. This is a common occurrence on these old Hondas ( and others) and requires that the powerhead be removed from the oil case and new exhaust gaskets fitted. When this happens, it afford one the opportunity to clean the oil sump and filter and many choose this time to assess and repair/replace internal engine components like main and rod bearings.
There's a couple of ideas to check out. And, while it could still be a carburetor problem, I see these as more likely given the symptoms you've listed.
Let us know what you find and
GOOD LUCK!