I'm having the same problem, I would really like the menu to be visible all the time.
Your "problem" (which is not a problem, is how GSX has been designed), doesn't have anything to do with the problem (real problem) discussed here, which is the menu closing *immediately*, caused by the issue I already explained of having manually copied the packages by mistake.
You are asking something completely different, like a "pinned" menu, and it's not how GSX is supposed to work.
The whole point is NOT having the menu covering the instruments and, most importantly, since it responds to numeric keys, not interfering with the operations in case those keys are used by something else (they are).
So, instead of an annoying menu you must always move to be sure it's not covering some instrument you might need to use, we have a smart menu that has different "timeout" times, longer for some operations and shorter for others, some with a default choice that makes sense so you can use it more "hands free" (like the operator selection) others with no default choice which just close without doing anything if you let the timeout expire.
This because, the whole concept of GSX is you call it to start some operation, and you won't need to use the menu again for maybe several minutes, so it wouldn't make any sense to keep it open to show...a menu, it's not like a navigation program that has a reason to stay open because it's showing ever changing info based on your position.