It isn't super high. It shouldn't be above zero, unless like Juice said, that your tap water gives a false reading. But your OP says you usually get readings of zero when you test? Which confuses me.
A reading of 0.25ppm for ammonia shouldn't be high enough to make your betta this sickly. But the concern is that the ammonia may have been higher than that yesterday and today before you tested, but has since been lowered by the filter and live plants. It's possible to have an ammonia spike and not realise until you catch the tail end of it with a test, but by then, the fish can be quite badly affected.