Disclaimer: I have only been fiddling with fixing pens for maybe a year or a little more, so read this and then look around for confirmation before trying anything you're not familiar with.
If something is blocking the feed, a bulb syringe can blast water through the feed to clear it out. That might work well after soaking that has softened up whatever is blocking the feed. As the shampoo bottles say, rinse and repeat as needed. Also an ultrasonic cleaner would probably help if you have one or can borrow one.
But this also sounds like it might be the nib not seated properly against the feed, so that the capillary action is interrupted (I'm not familiar with this pen, so I'm assuming it's an open nib pen, not hooded or semi-hooded or inlaid). I've had that a few times after I've had a nib and feed out, and it always reacted just like your description, writes for maybe a few words then dries up. Basically if you look at the nib end-on from the front, there should be little to no discernible space between the nib and the feed. If there is space there and/or if the nib feels at all loose, there's a good chance that might be your problem.
Fixing this can be a little tricky if you haven't done it before. In every case I have had, it needed to have the nib pushed in just a tiny bit more, and you have to be careful when you do that. Take one of those rubber grippy cloths and fold it over, or any folded cloth you don't care about getting ink on, use the cloth to protect your fingers from the sharp edge of the nib, and push gently but firmly on the shoulders of the nib (never the point!), straight in towards the pen. When I have done this in this situation I have always heard or felt a tiny bit of give and then the nib was firmly in place. I did this just a couple of days ago on an Osmia nib.
This can possibly result in a misalignment of your tines if you put any sort of angle on your pushing, but that is fairly easy to fix. The Pen Habit has an excellent video on how to do that, and I think Goulet may also have a video. You'll need to check the tines under magnification to be sure.
Disclaimer, just to refer you back to my disclaimer at the top. There are many experts here and if they tell you I'm full of it, probably best to believe them.