How should I respond to someone who says "enjoy the rest of your day"?

The phrase is almost always a neutral exit, so the real signal is in the thread that led to it. Scroll up and look at how quickly she was replying, whether she asked you anything back, and whether the messages got longer or shorter over time. A conversation where she was asking follow-ups and laughing at your jokes ends differently from one where she had been answering in a word or two for a while.

Also check whether she gave you a reason for leaving. A meeting, a commute, or dinner is an ordinary exit and tells you nothing about her interest. If she mentioned something she was looking forward to, like a trip or a show, that is a natural hook to come back to. The sign-off itself is just the wrapper. Judge the content above it.

When someone sends a short goodbye, a short answer is usually the right shape. The job here is to match her pace, close the loop warmly, and leave the door visibly open without pushing through it. One kind of reply is the simple close: a brief acknowledgement that returns the warmth and lets the conversation end cleanly. You can tell a draft is this kind because it contains no new question and nothing that asks her to commit to anything.

A second kind is the small hook. It is still short, but it points at something specific from earlier in the chat, so she has an easy reason to answer later. You can tell it is this kind because it refers to a detail she actually gave you. Leave out any compliment that is too big for the moment, and leave out anything that sounds like you are asking her to stay. A third option is to say nothing at all, which can be fine when the thread was already winding down and an answer would feel like you are reaching for the last word.

Send your reply within a reasonable window, the same day if the chat was active, and then stop. If the conversation was warm, one reply is enough. The next move belongs to her, and a message that arrives after a long gap will land better than one that tries to restart things immediately. A gap of a day or two is normal with most people, and nothing about it means she has lost interest.

If she does not write back, leave it alone for several days before you consider anything else, and make sure any later message has a real reason, like a link to something she mentioned or a plan you are proposing. If you have sent two messages with no reply, stop. Silence after a sign-off is the answer, even if it is an unsatisfying one. Moving on keeps your dignity intact and leaves the door open if she later comes back on her own.