If there's no new additions to the tank, didn't miss a previous water change, no left over food, faecal or decaying matter, then my guess would be to focus on your filter. Does you filter have any carbon elements to it, like carbon cartridges, etc? And when was the last time you cleaned it? Have you ever cleaned your filter with tap water?
I had the exact same problem with my tank (however I knew it hadn't cycled yet), where even if I did daily 30% water changes, the ammonia reading the next day would still be 0.5. I discovered that the source of my problem was with my filter's carbon cartridges. Basically, after a while, a carbon cartridge will 'expire' (typically after 3 weeks), for lack of a better word, and start to actually pump out toxins back into the tank. I got rid of the carbon cartridge and replaced it with just filter wool, did another water change, and the next day my ammonia was finally 0.
As for cycling, once the ammonia problem has been solved, you may have some problems getting the tank back in order. The reason being is, just like other aquatic animals, the species of bacteria that converts nitrite to nitrate cannot survive in the presence of ammonia. So because of your high ammonia readings, that bacteria colony may not exist, or it would take some time for it to do its job again due to low numbers.