Modern Vespa

Hi everyone! Can you help! My normally reliable 500 has become difficult to start in the mornings.
There are no odd lights or noises, everything is as it should be.
When I try to start it up it fires ok then immediately dies, every time I try after this it gets progressively better (i.e runs a little more) till after say five attempts it starts just as it should. I'm not using any throttle of course just pressing the starter button. It feels like fuel isn't making its way to the injector. I've checked for a vacuum in the tank and none has been found. I also swapped the hidden fuse relay and it's companion and that made no difference (just in case they were beginning to fail)
Looking through the old owners notes I notice the valves haven't been adjusted for a while. Maybe that's the problem?
Any thoughts! I'd add that once the engines warm it starts fine and ticks over without stalling. On the road it runs as it should. Plugs changed recently. I'm perfectly happy to strip off the panels to investigate problems (it's really not difficult!) but don't want to start this till I hear from yourselves! Thanks in advance!

Clean the throttle body's idle air bypass:

https://cheekythoma3.wixsite.com/itsme/idle

Thanks for the swift reply and advice! I really appreciate it!
A pleasant few hours were spent removing and cleaning and the bike now starts as it should.

Well just great….it's gone back to the same old slow to start problem!
I've adjusted the valves which were a little tight and removed the throttle body again to clean in case I missed something (don't think I did) Once it's been on a run and I restart the engine at work (lunch time) it starts on the button to go home later. It's the first start of the day on a cold engine which seems to be the problem. Any ideas??
Air filter and plugs are good. Runs fine once started!
Is my throttle body dying slowly? Any thoughts appreciated!!

I've heard people have had to clean the throttle body bypass several times until it cures for good.

Try the 'squirt while running' now you know where the bits are!

Thanks! I've ordered up more cleaner and will report back when I get a moment to have a blast with it! Probably a good idea to remove the air cleaner pipe work and spray into the throttle body and bypass hole yes? Rather than just spray into the opened air filter box.

Yes, you really want to get the spray getting well into the bypass hole. If you stand on the right you can blip the throttle while spraying into the hole. I'd have it on the centre-stand, with tilt-lock off.

Well! Despite the throttle body looking clear internally after I'd previously cleaned it out and after few good long blasts of cleaner into the idle hole the scoots now starting on the button again.
I've absolutely no idea what it might of shifted (there was nothing obvious )but for now it's back to normal!
Thanks for the pointers!

Thanks for reporting back.

Welcome to Italian dependability. Today you win, tomorrow you lose. That's just the way it is. Whaddaya gonna do, eh.

looks like I'm spending the bank holiday getting dirty hands because the problem is back! Just great! I really gave the thing plenty of good blasts whilst running (nearly a whole can) making sure it all went into the bypass hole etc. the metalwork is so clean now you could eat your dinner off it! Seeking inspiration from anyone with an idea or two!!
The only positive is I'm getting REALLY good at dismantling

Got home from work early and decided to start from scratch.
Panels off (hands too big for the tiny service hatches), check and adjust valves again, throttle body off and clean again because why not!
Nothing obviously out of place anywhere in the engine pit.
Throttle body back on.
Bl**dy thing starts first time. I've absolutely no idea why, which makes all this massively frustrating! Another cold start tomorrow morning will be the real test!
Hard to believe maybe a smidgen out on the valve clearance would possibly be my problem, but they all checked out ok to me!
But of course I live to learn……..