Last week I emailed a professor from my undergrad whom I was close with to say hi and inform her that my undergraduate thesis had been published. I am currently in a master's program and asked her if she would be willing to write me a letter of recommendation for upcoming PhD applications for next Fall (and it is worth noting that she wrote me a letter of recommendation for the program I am currently in). She has yet to reply and having a letter from her would really strengthen my application. Is it in poor taste to resend her an email, or should I move on? Like I said, I would really like to have her letter as part of my applications.
Unless your request is urgent, you should wait two weeks from the date of the original email for your follow-up.
The subject line is easy, it will be the same as the original, but prefaced by "Re: " (which is automatically supplied by most email programs).
Alternatively, if there is any other topic you are interested in corresponding with her about, you could write to her about that, and at the end ask her if she's okay with writing the LOR.
In either case, you can make clear in this new email what the deadline for the LOR is, but explain that you'd like to line up your references before, for example, the end of October, if possible.
You should absolutely follow up with her. At this point you have no idea why your email did not get answered. She could be at a conference. She could have missed it completely. Or she could have meant to write you back and simply forgot. I'm in my last year of grad school and none of these things are particularly uncommon for professors. Do not waste time wondering about why she did not write you back, simply reach out to her again. Your letter should say something like this: "Hi Professor So and So, I'm following up with you regarding the letter of recommendation for my graduate school applications..." When this has happened to me I almost always get an immediate response with a flood of apologies for the late reply.