Unless I'm just using bad grammar I guess, it feels more natural when talking to someone to say "zero point five days" when referring to 0.5 days; conversely, it sounds more natural to say "one day" when referring to 1 day.
A similar question might be relevant: Why do we say "half a day" when describing the value, but "zero point five days" when being numerically specific?
It might have to do with the fact that plural units are a numeric consensus where the singular is the exception. That's largely related to the fact that the idea of one-or-many existed before the (widespread) concept of Math (and mathematical subdivisions of an item) and the concept of zero in many cultures and languages. Relative subdivisions of a whole were largely considered independent units, especially in (but, again, not limited to) English. Consider and compare 0.5 days to half day, or 0.25 days to a quarter day.
I personally find it odd to use the singular noun on something that is not a singular unit, even if it is part of a singular unit. However, such examples do exist, and people would be prone to verbally append of a between the numeric and the unit, such as 0.5 (of a) day whenever encountered with a written 0.5 day.
Short answer? English is a bit weird and there's no real consensus on the matter.
According to the AP Style Guide, when the decimal is 1 or less, the singular should be used. The Chicago Manual of Style disagrees, and uses the plural.
As far as "why isn't there consistency?" goes, I don't know that you'll find a real answer outside of the fact that language evolves and sometimes it's a messy process without much logic behind it.
