Check the fuel lines make sure they don't have any crud in them, do you have inline filters? I have a 125 that was doing the same exact thing, turned out the line was full of crud, it would bounce down into the inline filter and if you just idled or putzed along slow the fuel flow would catch back up and you could go again. You could rig up a new chunk of fuel line to a bottle of gas, i use a washed out a gear lube bottle as the fuel line will push over the nozzle tip. See if it runs ok. I believe the 110 has the same carb as the 125, make sure the strainer is clean and with the petcock off the carb put a bucket under it and try both the on and reserve positions and make sure you get fuel flow, they cause troubles and you can get a new rebuildable petcock off ebay thats held together with screws instead of rivets so it can be taken apart and cleaned. Sometimes they get crud in them also.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....