what causes a starter to stay engaged

Sounds like a classic stuck solenoid. I had the same issue on my 2008 Yamaha Grizzly. Replaced the solenoid and it fixed it. Check the battery connections too, loose grounds can cause weird electrical gremlins.

Could also be the starter relay sticking. Sometimes they weld shut internally. Tap it lightly with a wrench while it's stuck to see if it releases. If it does, replace it immediately.

Don't forget to check the starter itself. If the bendix gear is sticking, it won't retract. Pull the starter and clean the shaft, lube it lightly with white lithium grease.

I disagree with just replacing parts. First, test the solenoid with a multimeter. Check for continuity when the starter button is released. If it stays closed, solenoid is bad. If not, look elsewhere.

Had this on my 2010 Honda Rancher. Turned out the starter button was sticking. Sprayed contact cleaner in the switch housing and it's been fine for two years. Cheap fix to try first.

Check the starter motor brushes too. Worn brushes can cause the starter to hang up. If the commutator is glazed, a quick cleanup with sandpaper might help, but replacement is safer.

Make sure your battery is fully charged. Low voltage can cause the solenoid to chatter and stick. Load test the battery before throwing parts at it.

I've seen the starter clutch fail on some models. If the one-way bearing inside the starter drive is seized, it won't disengage. That requires pulling the starter and replacing the drive.

Before you go deep, check the wiring harness for chafed wires. A short to ground can keep the solenoid energized. Look near the frame and engine mounts.

Could be a bad ignition switch. If the switch doesn't return to the run position properly, it keeps power to the starter circuit. Test with a multimeter at the switch.

I had a similar issue on my 2005 Suzuki King Quad. The starter relay was mounted near the exhaust and heat damage caused it to fail. Relocated it and no more problems.

Don't overlook the starter motor mounting bolts. If they're loose, the starter can shift and bind the bendix gear. Tighten them to spec and check alignment.

If you have a winch, check the winch solenoid too. Some are wired into the same circuit and a failing winch solenoid can backfeed and keep the starter engaged.

I'd recommend replacing the solenoid with an OEM part. Aftermarket ones are hit or miss. I tried a cheap one and it failed in a month. OEM lasted years.

Check the starter relay fuse. A blown fuse can cause weird behavior, but more likely it's the relay itself. Swap it with a known good one if you have a spare.

Had a buddy's ATV do this. Turned out the starter motor was internally shorted. Replaced the starter and it was fine. Check for excessive current draw with a clamp meter.

Make sure the engine is properly grounded. A bad ground strap can cause current to find alternate paths, keeping the solenoid engaged. Clean and tighten all ground connections.

I've also seen the starter button get stuck from mud or debris. Pop the button out and clean it with electrical cleaner. Sometimes it's that simple.

If you're mechanically inclined, pull the starter and bench test it. Apply 12V and see if the bendix extends and retracts smoothly. If it hangs, rebuild or replace.

One more thing: check the starter relay diode if your model has one. A failed diode can cause the relay to stay closed. It's a cheap part and easy to replace.