I'll check my schedule.
In other words: "I don't know yet if I'll come, but I don't want to say NO right now".
Possible causes for that answer are:
I'm not sure I'll have time.
I'm not sure I'll enjoy this.
I'm not sure I can put this on top of my priorities.
...and so on...
The other person may think that it's none of your business to know the real ...
I run into this problem because I have an old friend (all the way back to grade school) who lives 3 time zones off from me. We like to have long calls on the weekend every month or so to catch up, but scheduling them can be a bit of a pain due to the time difference, and the fact that I have to cram my non-work life into weekends, so lots going on.
I understand how this feels, and I've been the person that says that they will check their schedule. I also often forgot and had the other person remind me.
What I can say, it helps me to let me know why you want an answer now. If you do that, you create some sense of urgency with the other party. If you didn't, then I would indeed forget.
Two situations ...
Dealing with recruiters, potential bosses, etc., can be hard. I once completely missed a job interview because I (also) entered the incorrect time into my calendar. I was embarrassed, and I worried about what the interviewer would think about me. However I quickly called him and told him honestly what happened; he said that he was glad that I called, because ...
What can I say to "I'll check my schedule" to get a more definitive response?
If I may, I would reframe the question as,
What can I say to avoid getting an "I'll check my schedule" response?
... to which I would answer:
Set a deadline.
Simply add, "RSVP by [date]" to the event invite. At that point, it is assumed that everyone will "check their ...