When failure to pray becomes a sin is when we put other things before God.
If you say I was going to prayer, but I was too tired because I had basketball, then beers after the game, and finally had that movie I had to watch than might be a sin. On the other hand making the attempt even when tired is a good thing. Even if we are not giving everything to God it is not simply because it wasn’t high enough on your priorities. Now if you always find you are passing out 5 minutes into prayer then I would suggest finding a better time to pray or looking at what other things you could reduce to relieve some of the pressure on your time.
Sometimes the best option is setting 30 minutes for prayer at the same time every day. Personally I find if I don’t make the time then other things can start to creep in and push things out. It’s a little like planting a garden and not keeping an eye on it. After a few weeks of neglect weeds can start to invade and choke out the plant’s you wanted to nurture.