Can it happen? Anything can happen; and for what it’s worth, Greek has even gotten rid of “once”: Ancient hapax, dis, tris, Modern mia fora, ðio fores, tris fores “one time, two times, three times”.
But as Mike Richmond argues (Mike Richmond’s answer to Will the word “twice” become archaic like “thrice” has?), there do not seem to be clear signs of twice perishing quite yet. The spread of two times in American English that others have pointed to is interesting; watch this space!