Okay so I know for a fact that I'm due for some badges. Like the bronze medallist badge (I have made well over 300 medals at the island) As well as some encyclopaedia related ones. Phineas has not been in my town for weeks though. I've read around and someone said he doesn't show up if its rainy/overcast? Which it has been in my town.
Your post is kind of confusing. Has it been rainy / overcast the last few weeks? If so, that's why he's not showing up. You just have to wait for a sunny day which should happen soon since July is usually sunny. The only other reason he wouldn't show up is that you haven't actually fulfilled any badge requirements.
For the first time he showed up when it was overcast in my newest town. I have 4 towns and this is the first time it's happened.
About an hour later the sky cleared up.
Just as I clicked this, the weather cleared up today and Phineas came in town. Just keep asking him for all your badges again and again. Guess the guy hates rain.
1. It's possible that you're mistaken on either the badge requirements or what you've actually accomplished. Like I thought that I was due for my dream suite badge but it turns out that I hadn't been to as many dream towns as I thought I had, so I had the same problem you're having.
or 2. you're missing phineas? like it's possible that he's been there but you haven't noticed him being there. This seems unlikely but it's probably happened to me before.
Even if it isn't raining when you play, if it at all is scheduled to rain that day by the system, it rained- even if you don't see it. We've just had the rainy season (they based this off Japan's rainy season), so in a few days when we get clear skies (even the Japanese one says they're coming), you'll see him showing up. Basically he won't show if it's scheduled to rain that day.