Okay I have the same adapter. The problems with it are multiple:

1. The pin is not wide enough, causing the v-shaped plastic pin on the sodastream that is meant to depress the valve pin to slide off the side of the valve pin half the time.
2. The pin, at least on mine, is cocked to one side (doesn't come straight out the center of its mounting hole). This is also causing/exacerbating issue 1.
3. It is not adjustable. I've heard people talking about ones that can be adjusted because the pin is a screw. This one is not, which sucks. If anyone has a link to an adjustable/serviceable/maintainable version of this adapter please please let me know!
4. The pin does not go up high enough, causing you to have to push the button down further than desired, almost to the point where I feel the cheap plastic on my sodastream is about to give out.

Problem 4, the one you're having, may be solved by adding material above the plastic pin, between the button side's leverage and the plastic pin. On my fizzi, this has meant disassembling the entire sodastream to be able to pull the button-lever back far enough to wedge two dimes into the gap (where they will hold themselves in place due to the width of the side walls of the lever). It is not an ideal solution.

Unfortunately I'm at my wit's end with this fizzi. Taking it apart was HORRIBLE. The valve/button/lever piece is held in such a way that you have to access it from the back to remove it, which means taking the entire front mechanism apart to get access to the retainer tabs, then using TWO thin metal shims simultaneously to push back the two retaining tabs. It's the most infuriating design I've come across (in the last few days lol).

All this to say, please let me know if anyone has found a better adapter. I've tried this one which I bought first, but both it and its warranty replacement from the company leaked like crazy, so I tried the brass one which seems to have its own issues.

Or perhaps it's the fizzi that is making this so difficult, but I got it for $5 at a thrift shop so spending real $$$ on a new device for this would be disappointing. If anyone has better recommendations in that direction let me know... I'm aware the fizzi is plastic trash.

Please tell me you've found a solution!

P.S. I plan to upload a disassembly guide to iFixit as there's no information I could find anywhere for how to fully disassemble the fizzi.

EDIT: Anyone tried this adapter? Looks adjustable, but would need to buy a CGA320/Type30 quick connect nipple adapter for it for my existing hose...