ASA hydrolyzes rapidly in aqueous solution; therefore, it's not stable enough for an injectable (also why there isn't any oral solution formulation). The ASA in Alka-Seltzer goes into solution, but is meant to be administered as soon as the tabs dissolve, so within that time frame it's ok. Sublingually, there may be a problem with absorption because of ASA's acidity. Once it goes into solution it's going to be ionized at the pH of the oral mucosa (not a problem in the stomach where the pH is actually low enough to get the majority of ASA in its unionized state).
Just a guess.....🙂, but I'm pretty sure I'm right.