Should I give up on her?

I've known this girl for about a year and a half but we've just recently realized we like each other as more than friends. She's a lot of fun to be around and I'd really like to see where it goes (and she's said the same) but so far we've gotten nowhere. It's been about 2 months since that happened and we still have yet to go on an actual date, despite me asking her out once or twice a week.

She's got a great job and a son that's 8. I understand that they are both time demanding and don't want to interfere with either, but I'm having a hard time believing that she couldn't make it once in 2 months if she really wanted to. We've met up for coffee and lunch a couple times but nothing beyond that has worked out.

When I ask her on a date she always says that she'd like to, but something always fouls up the plan. She can't find someone to watch her son, she already has plans with friends, she's got work to catch up on, etc. Once or twice she's said she'll try to get a sitter and get back to me and never has.

I haven't yet had the balls to ask her what the deal is because I'm worried it'll sound like I'm "blaming" her son and/or work. What's the best way to handle this, Reddit?

*edited for grammar

"Decision" edit: Thanks internettor and FromTheSky. Looks like that's the consensus. I'll cease with the asking out and leave the ball in her court. Appreciate the comments guys.