I've had my wallet out for over a week now and I'd say 95% of my minted coins come through just fine.
I know I made a big deposit about 17 days ago so I was going to leave it open until the 20 days passed for that but I don't see a problem with having it open 24/7?
Minting perfectly for me with it open 24/7.
I have been leaving it open 24/7 but it chews thru resources. And I'd say I only get less than 10% with any confirmations, I have up to 200 mint transactions generated now from what I hold. It sounds like its better if I just open it every few weeks. I thought I would miss out on transactions if I had it closed. I mined it since day 2 of coin being released.