Interactive or rendeding?
You probably encounter a mem overflow. Avi is cetrainly not the best possible format for fetching frame so and so i(nfact it may indeed be one of the worst possible ones,baceuse it may need to read in much more than absolutely minimaly needed). Its more lika badly indexed bunch of files. Also cosider rendering your stuff on small batces at a time it will save your ass oneday.
Dump the animationa s a sequence of individual images since the avis uncompressed theres not much more overhad but theres a lot maya can do about it. Such as turning them into bots/maps/tex files (depending on your rnderer of choise) wich may be REALY REALY beneficial.
BUt a notable side note: Texturing and producing end images are wastly different things. Firstof its often very rare indeed to need textures that are more than half the size of your final output. So if your renered output is 1280x720 you can probably get away with 512*512 or 1024*1024 images. Note while the 1024*1024 omage is technicaly speaking larger than yourofrmat its SQUARE nad powers of 2. Square textures like this usualy use memory far better than non sqares. Infact id be highly sceptical of any texture NOT square or atleast squeres next to eachother such as 512*1024 And all powers of 2 offcourse.
Now then let me explain a concept of what gets hit whan you render, se making higher res dont ensure better /crisper / more accurate images. The only thing they esure is MORE memoryhogging. For stills they do tend to produce nicer imagery by default however especialy whan you choose yoru filtering wisely. But for animation bigger sizes usualy end up cassing a lot of havoc to setting a good filter/speed/quality/fliker freeness ratio. Especialy on noisy imagery.