Well, if the back third of your tongue is pressing against the soft palate AND you didn't have proper forward development, that's it, you'll not be able to breathe. I can't breathe either when I press the back of my tongue against my palate: I had bad posture, forward neck, braces, mouth breathing and low tongue position. BUT there's a catch to it:

First: You need to make a distinction between you not being able to breathe because of your tongue and not being able to because you're holding your breath thinking you are pressing the tongue against the palate. How do you do that? You gotta get conscious about your tongue and mouth for a few days so that you develop a sense of your tongue and control it better.

If you hold the back of your tongue up while holding your breath your uvula will get VERY irritated and painful (personal experience).

Now that you know which one is which, you gonna need strength in your tongue hold it up there. Tongue chewing is the answer. Basically you get gum and squeeze it against your palate with your tongue as hard as you can. This will build strength to your tongue to be able to stay in the palate. (Dr. Mike Mew's video about tongue chewing: click)

Cool, that's a lot of stuff but it didn't give you a solution, right? The thing is: while having proper tongue position, we'll not be able to breathe until we have enough forward growth. To mitigate this situation, at least for me, there are two possible ways:

1) Hold the back of the tongue up but just enough so that you still can breathe. Hardly but still.

2) Slow your breath pattern. Between one breathing and another you lower only the back of the tongue so that you can breath and right after breathing press your tongue up again (Breathe in / Press your tongue up / Breathe out / Repeat).