Why is it often spelled with an a? Well, let me theorize here. Maybe it's some sort of genetic Indo-European memory? You see, Existence - I'd have spelled it with an a if not told otherwise - seems to me to be a Greek word, or something related. At any rate, it seems old Indo-Eurpean. Why? The 'ste' part of it. In Greek, histemi is 'I stand' or 'I place' - and can be used to denote falling into a certain state of being, ie. falling into the state of war. The thing is, it is a bloody irregular verb. The present might go histemi, etc. but the past is, if I remember right, built off of... okay, I'll go check it out exactly. There we are, present: histemi, histes, histesin, histamen, histate, histasin. The present shows what I"m talking about in those last three (the plural, ie. 'we; you; they'; the first three are 'I; you; he/she/it') the 'ste' becomes 'sta'. It is an Indo-European quirk, and is called, if I'm not mistaken, an ablaudt, discovered by the brothers Grimm I believe. The point in this is, if existence does indeed come from that root (I think I will forthwith check), the e and the a are a bit variable. Existance might not be so far wrong... etymologically speaking, that is. Technically, it's still wrong. But maybe those of Indo-European descent innately have a desire to switch around a's and e's like that. Maybe that's why we mess that one up.
Oh, and as a side-note, that 'ste' root doesn't only exist in Greek. In German we say 'ich stehe' (I stand) which also in some cases changes to 'a' (ie. gestanden or some past perfect or something like that). And English is no exception. 'I stand.' Or, I suppose, the word 'stance', as well. There, that must be it. People are taking it to be exi-stance, thinking like someone in a state of being. In a stance. Ironically enough, though our technical spelling is different, they may not be wrong in thinking like that. I'll have to check it out, but if the word does come from that Greek/Indo-European root, then existence does, in fact, have very close ties with the word 'stance' and is, probably, the selfsame word spelled with an e instean of an a. What you're getting is people's mind going towards the more common English usage of the 'ste/sta' root, the spelling with an 'a'. Existence is, I believe, the anomoly.
There, is that a proper explanation for the mis-spelling? I think it is a good vindication of the 'existance' spellers.
UPDATE:
Okay, got it. I was close. It's not from Greek, but Latin (both of which are Indo-European, so I was right on that front.) The origin of 'exist' is ex-sistere. 'existence' is the present participular form, ex-sisterem, I think it was (exactly what it was slips my mind; you get the point, though.) The dictionary points this out to be a reduplicated form of the 'ste' root (ie. ste redulplicates to siste, reduplicating the s and putting an i inbetween.) As a side-note, in Greek this reduplication is also done, but they have the odd tendancy to turn an s into rough breathing (our h... the Greeks didn't consider it a letter.) Thus it's not 'siste' but 'histe' (remember the 'histemi I mentioned earlier?) That sort of thing is also seen in the word for 'I lead', in Greek hepomai, and Latin sequorem. The h for the s, and the older qu preserved in Latin in place of the later p which the Greek uses. Anyway... back to what I was saying, this means that the word existence does, indeed, stem from that old 'ste/sta' root, and uses the 'ste' as that is what it is in Latin (or, at least, in the Latin from which we get the word.) However, our English brand of Indo-European tends far more to the 'sta' root. So, in a sense, one might say that in saying 'existence' one is following the Latin root, whilst those who say 'existance' are in fact Anglisizing the word to follow English Indo-European convention. Just like we'd not say 'stend' but rather 'stand'. It is, therefore, a very reasonable mistake, and other than the cause of tradition which has us spell it in the Latin way, reason dictates that 'existance' is a more locial way to have it spelled. We are speaking English, after all. It's like as if we, for some reason, preserved the old Greek Alexandros in place of Alexander. It has become fossilized in our vocabulary, but there should be allowance for spelling it in a way that is more 'English.'