How to suggest a date when she keeps saying she's free sometime but never confirms

"Sometime" with no day attached is usually a sign that she hasn't thought about the logistics, or that she'd like to see you but isn't going to be the one to organise it. Neither of those means she's losing interest. But if she's said it twice and you've still got nothing on the calendar, the pattern is telling you something. The answer is to stop waiting for her to produce the plan and make the plan yourself. Look at the next week, pick the evenings or weekend slots that work for you, and put them in front of her. Then see what she does with them. If she engages with one, you have a date. If she answers with a different vague line, you have information about how much she's investing in this.

The second thing to watch is whether her replies get shorter when you move toward a specific ask. People who are interested usually respond to concrete suggestions, even if they propose a different time. People who are polite but unsure tend to keep the conversation pleasant without picking anything. Notice which one you're getting.

A single proposal can feel like a test, because she has to accept it or turn it down. Two options feel more like a choice. Name a day and a rough time, and name a second day as a backup. Keep both inside the next week or so, since anything further out makes it easy to drift. Choose something specific to the place or activity, not a general "drinks" or "coffee", because a named plan is easier to picture and easier to answer. Make the ask short and leave room for her to counter. If she proposes a different time, that's a yes. Shift to the new time and confirm it in a single line rather than negotiating back and forth. Keep the number of options to two. A third one starts to read like you're waiting for her to pick from a menu.

If she doesn't answer your suggestion, give it a full day before sending anything else. Many people read messages in batches and reply when they're free, so a quiet afternoon doesn't mean she's ignoring you. When you do follow up, keep it light and don't repeat the whole proposal. Something like confirming one of the two options you already named, or asking whether either still works, is enough. Don't send three messages in a row or ask why she hasn't replied. If you've followed up once after a day or two and still have nothing, drop the plan for now and reply normally to whatever she sends next. If she brings up hanging out again, you can suggest a specific time then. If she never does, you've got your answer, and the sooner you accept that the better you'll feel.