You need to isolate whether it is (broadly) a fuel issue or an ignition issue.
Easiest way is to check for spark when it won't start.
It is possible that the stator is starting to go (possibly cracked). When it warms up (after running) the windings expand and loose the ability to provide enough power to get it to fire. This is not super uncommon. Even these small models have separate windings that provide low and high (rpm) power.
Above 2500'ish rpms the high speed winding may provide enough power to fully compensate for a somewhat degraded low speed winding (which "always" provides power), but once it's heated up and the low power coil no longer functions at all, you don't have enough power to create a spark until after the motor cools down again.
Another trick to check the above scenario is 1) remove the top cowl (hood) 2) grab the wife/girlfriends blow drier 3) use it to heat up the flywheel until is as hot as the hair dryer will allow (heat gun works better if you have one) 4) try and start the motor with it heated up - if it's a "no go", the stator moves way up on the suspect list.
And the 6/8/9.9 Merc's with the throttle/shift in the handle were built from late 1985 (sold as 1986 models) all the way up until the 9.9's were completely discontinued in 2012 (internationally), about 2005 in the US.
