Should I give her space if she pulls away

Start by separating what she did from what you assumed it meant. Slower replies, shorter messages and a cancelled plan are three separate signals, and they carry different weight. A cancelled plan with a stated reason is mostly logistics. A string of one-word replies with no questions back is more likely a sign she has less energy for the exchange right now.

Look at whether she still starts anything. If she shares a small detail, asks you something, or references a joke from earlier, she is still in it at some level. If every message is a closed answer and she has stopped volunteering anything, that is a clearer signal that the pace or the interest has dropped. Both are normal. Neither tells you what to do yet, so the next move should be low-cost and easy to ignore.

Once you have read the signal, your options are roughly three. You can send a light message that refers to something specific from earlier, which tells her you are still around without asking for a response. You can wait and let her make the next move, which works well if the last exchange ended on a clear thread. Or you can make one clean, low-stakes proposal with a real date or a real activity in it, which is useful if the plan has been loose.

A draft is the right kind when it takes the pressure off. It should contain no question about her feelings, no apology for being in touch, and no request that she account for the gap. If your message would still make sense to her if she never replied, it is probably the right size. Leave out anything that reads as checking on her commitment.

Timing does more work here than wording. If she has pulled back, wait long enough that your next message does not look like a reaction to her silence. A day is often enough when the conversation was already slowing. Two or three days works when there was a cancelled plan and she gave a reason. The point is that your message should feel like it came from your own day, not from her absence.

If you get no answer to a light message, let it sit. Do not send a second one with a different angle on the same thing. If a week or so passes and there is still nothing, you have your answer, and the kind move is to stop. A short closing message that leaves things open without any hint of hurt is fine, but the strongest outcome is simply to get on with your week and treat any future reply as a fresh start.