I also have a Wren Anglo from McNeela in Ireland, which I bought in the summer of 2018 to serve me as my ‘beginners’ instrument. Sadly, it has also suffered from sticking buttons.
Here’s what I found – bear with me because I don’t have the correct concertina parts vocabulary.
As has been suggested already, you will need to take the end(s) off the concertina. (Be prepared for a disappointment at the standard of workmanship – mine looks as though it has been built by a first year apprentice on Black-Eye Friday!)
I found three issues related to the sticking buttons.
Firstly, when you remove the end(s) and have a look inside, you will see that the buttons have a hole at the bottom through which the rocker arm passes. The hole at the bottom of the button is shrouded internally with a small piece of rubber grommet, and on my Wren there has also been applied a very liberal amount of a very sticky substance around the grommet. This substance may be non-setting glue, or it may be lubricant, I don’t know, but let’s call it ‘goo’. With the constant action of the buttons, the goo on my instrument has migrated up the buttons such that when it has reached the internal surface of the wooden end plate it has stuck to it and thereby caused the buttons to stick. Using cotton buds and some ‘Sticky Stuff Remover’ (bought at Aldi years ago), I cleaned all of the buttons and removed the excess goo from around the grommet. I also cleaned the guide holes in the wooden end plate.
Secondly, because the only guide that the button has when it moves in and out is the hole in the wooden end plate, the button must be positioned on the rocker arm so that it is 90 degrees to the end plate. The tolerances on the holes in the end plate of my Wren are poor, and as such it’s possible for the buttons to come through the holes at an angle, which causes friction – wood against plastic as there is no felt bush - and this causes the buttons to stick and sometimes to jam. Many of the buttons on my Wren were misaligned. You can move the buttons along the rocker arm at the point of the rubber grommet to get them back into exactly the right position, but even then they might move over time.
The third issue relates to the position of the springs. On my Wren, there was a noticeable difference in the spring tension between various buttons with the weaker return tensions contributing to the sticking buttons. The top arm of the spring wraps around the rocker arm and is therefore captive, and the bottom one rests freely on the base plate. Some of the bottom free moving arms of the springs were set at a poor angle for them to be able to afford the best return tension, i.e. they were far off to one side. So I set them as best I could to be as near in-line with the rocker arm as I could get them, thus improving the return tension.
The buttons on my Wren rarely stick now, but it has been a deeply frustrating journey. I could have sent it back to Ireland as it’s under warranty, but that might have added to the frustration. (One of the reeds on mine sometimes doesn’t sound, but as of this moment I haven’t worked why that is). It’s a beginner’s instrument of course, and priced as such, but still not cheap. Nevertheless, it should still work properly and as beginners, we are more likely to give up if we find our instrument is faulty and of poor quality.