That's odd. Do you have alot of cedar and saplings? The fruit trees don't have eggs. I've played it and found abunch. Got about 8 or 10 tree eggs. Also you can save and quit. Send a 2nd character out and items will be reset.
I played in my 2nd real town. It's set 5 months ahead.
Set the bunny days in my holiday room. Kept 6 different eggs and put them in different places.
2.3 billion bells Town Victoria Name Mcnugget
Town Lazytown/ Stitch Town Lolly/ Stitch 2 Town Reality/ Queenbee