Kohler CV15V crankcase hose

Would a leaking hose cause the mowing not to start after not running for couple of weeks?
Mower will fire right up if I prime the carb, and start and run just fine if used before two or so weeks

too rich, too lean, or bad fuel

I should have added there will be not fuel getting to the carb after two weeks or so when trying to start
Prime it starts right and with start fine until it sits another few weeks

Assuming this is a carb model and not fuel injection, because you say it starts when you prime it, it is likely a problem with fuel, or the fuel-to-air ratio. But it can also be a combination of things. The only way to fully know is do some testing, or go thru a general service on it. My suggestion would be to start by draining the fuel in the tank and bowl, and fill it with new fuel. Maybe replace the fuel hoses and filter if you have one. At least eliminate that as a possible cause. Next step would be to rebuild the carb and check compression / adjust the valves if they have not ever been adjusted.

What you could be experiencing is the need of a general tune up, or it could be a specific one thing. Adding fresh fuel to prime it could be that it can run in a perfect environment but not in a marginal environment. Adding two additional weeks of sitting could be the pattern or it could be time of day and engine temperature etc..