The game provides a framework and guidelines for creating new magic items:
http://www.d20pfsrd.com/magic-items#Table-Estimating-Magic-Item-Gold-Piece-Values
However, these aren't really hard and fast "Rules" per se. Ultimately creating a new item is adding content to the game and that's at the
GMs discretion. Strictly speaking does the game provide rules that could be used to make a +1 Whatever of Whatever? Yeah. However if the
GM says it can't happen, it can't.
If I was to wager a guess I'd imagine the resistance to the idea steams from the fact that traditionally the items have only come in +2 Increments (at least since 3rd edition D&D), so a +1 or +3 type feels odd in that context. Similarly it may feel broadly "Gamey" to the
GM and the
GM may not be OK with that. At any rate it's still wholly the
GMs call and probably not worth raising a stink over.