The owl statue only gives you a temporary save until you are next ready to play.

To permanently save important items like the bow and arrow you have to do a permanent save by playing the Song of Time and returning to Dawn of the First Day. You will have lost all lesser items like potions, nuts etc. and any fairies you collected in a dungeon but didn't complete. But you will keep important items like the bow and arrow and any fairy upgrades you won if you returned all lost fairies before you retruned to the first day.

If you make an owl statue save and then return to the game and quit without making an owl save or a song of time save you will lose everything you have gained since your last permanent save. So if you haven't made any permanent saves then you will indeed lose everything. it's not that your game has gone wierd, it's just that the game has a slightly unusual save system.

I recommend completing the entire woodfall temple, getting all of the fairies and the bow and arrows, then getting you great fairy upgrade and returning the deku princess, then getting the mask of scents from the butler...

All before saving using the song of time.

In other words, don't expect to turn off the game after restoring your save and expect it to still be there. You'd have to go back to the owl when you want to turn it off, unless you can afford to go back in time.