Not something I’ve come across myself. Your logic sounds pretty good, though - air not getting back up would stop the ink flow after a while. I presume the Verve is a cartridge/converter filler? Are you filling the converter in the pen, through the dipped nib, or by taking it out and dipping the converter in the bottle?

If you’re dipping the nib, a paragraph might be about right for how much would be held in the feed and nib after dipping, without anything making it out of the converter. You could try dipping the nib right into the ink, then writing with it, and see how long you get then - if it’s a similar time, it might be you’re not getting anything flowing at all.

You could also try partially operating the converter again with it in the pen, to force some ink out through the feed - carefully, so you don’t get covered in ink ;) If that then works again for a while, the air pressure idea could well be right. Soaking the section overnight might be the best plan, just in cold water. Water with a little household ammonia is usually the next step.
Cross fountain pen ink doesn't flow

I have a Parker classic fountain pen I have sent to Cross twice because the ink stops flowing using their cartridges. When I use the converter with Parker ink it works fine. I would like to use the cartridges as I travel quite a bit. I have cleaned the nib at least ten times with no joy. Any ideas?
The only suggestion I’ve seen for that sort of situation is to use a little dilute detergent - washing up liquid - to flush it through a few times. Sometimes oils left in the feed from manufacturing can cause flow problems, and the washing up liquid will break down the oils. Might be worth a try, if you haven’t already done that.

Can I recommend that you use the pen regularly, daily if possible? You can also do the following, wash out the pen between each cartridge, use the converter to pump water back and forth through the mechanism. Sometimes I use the bulb part of a camera blow brush to force water through the nib.

I would be tempted though to give up on cartridges. They are a criminal waste of money and landfill space and instead change to bottled ink.

If it’s an Aerometric, they don’t usually need much doing - the collector can get blocked up, but the Sac is usually pretty reliable, and there’s nothing in there that needs specialist tools. The Vacumatic does need some special tools, but it’s supposed to be a very difficult fix - might be better left to someone who knows what they’re doing.

Firstly my fountain pen is an unknown model from China and I am sure you know the low cost fountain pen branded 'Parker hero 89-x'. I have one and it has gone through some things… I cleaned it with Cutex… is it ok?? My fountain pen the black thingy under the nib is a bit out of shape… how do you fix it back… and also…. If it is possible, could you send me a picture or diagram on how to align the nib?