Perhaps you've asked the same question. I'm guessing this question has also served to de-motivate many people in their prayer life. But far from God's sovereignty killing our desire to pray (because "God is going to do whatever he's going to do anyway"), it should bolster our confidence and passion in prayer. I'd suggest we change our thinking to this: "God is going to do whatever he is going to do through me."
That's right. God is going to save people as an act of his loving will through me sharing the Gospel with them. God is going to convict a sinner's heart and help them to see the hope found in Jesus Christ through me praying for them. God accomplishes his sovereign will through his people, who humbly share the Gospel, pray, and love.
Why else are we still here on earth? We're here because we are the means God has graciously chosen to use to accomplish his ends. It's pretty cool that he has chosen to work out his plans this way, that we get to be a major part of what he is doing.
I was thinking about this because someone emailed me asking this very question, so I'll post my response next which includes the Scripture to show this is the case.