Why do iPhones take so long to turn on when they die? How can I fix it?

I have an iPhone 3GS and I don't let it die very often, but when it does, I try to plug it in as soon as possible. Most of the time, it's only dead for between ten minutes and a half hour, and then only takes a few minutes to turn on. But sometimes, it takes a few hours before I have access to a charger. When it's dead for a long time like that, it takes hours to turn back on. It happened worst a few days ago, when it died and I couldn't charge it for five hours or so. When I finally got it plugged in (before I went to bed at about 11:30 PM), it wouldn't turn on so I decided to go to sleep. It woke me up at about 4:30 AM (which I really didn't like) from missed calls/messages. Why is it that it takes so long to turn on? Is there a way to fix it?

Well if the battery is really low it doesn't have a sufficient amount of power to turn itself on.

you see, turning it on (booting) requires a lot of power because the booting is when iOS is setting up and preparing to run all of the features of iOS. So a lot of power is needed.

so when the battery is really low on power iOS can't function properly, lagging the process.

if it's not working properly charge for about an hour or 2 and restore it with itunes.

and if that doesn't solve the issue + it's still under warranty have apple fix it.