Is it true..

Is it true that if you abstain from sex for ____ amount of time, that your ability to get hard will diminish? If so, how many weeks or months are we talking about?

No, it isn't true. Although, if you wear a chastity device long term it can affect your ability to get a full erection.

I've read that here about the chastity belts, but I still wonder why it would be different if one just abstained.

The chastity device prevents you from achieving a full erection (if at all). Over time it will affect you're ability to get a full erection even when uncaged. I'm not sure what the exact physiological causes are.