Legally, she could have remarried, as far as I'm aware. I have never read about a restriction against her potential remarriage.

As for why not ... there are a number of potential reasons. For one thing, Anne was in a very good position as "the King's Beloved Sister". She was independent, she had been given her own household to command, and she had a great deal of property and money. If she were to marry again, she would be under the authority of a husband and would potentially lose much or all of her autonomy. She may have been seen as a tempting prize, but also one dangerously close to a king who'd proven himself to be fickle about his loyal supporters. She was also quite a bit higher in rank than any English noblemen, given her background, and so may have personally been opposed to any marriage in her new country, while perhaps also not having the ability to get a marriage arranged at her proper rank outside of it by virtue of no longer being her family's dependent.

But on another level, this is similar to the case of Catherine of Valois, which I wrote about here:

Unfortunately, we don't really know why Catherine of Valois married Owen Tudor. This is really the case when it comes to a lot of personal motivations in the Middle Ages: remember, unless someone writes down their thoughts in some form, like an intimate letter or a journal, they are lost. And in periods where such things were not terribly common, and which are far back enough that many documents have been lost anyway, we rarely know individuals' personal motivations.

To be honest, we barely know that they got married! In 1422, Owen Tudor took up a position in Catherine's household after the death of Henry V, which left her no longer queen consort but dowager queen mother, a step down in prominence and importance. In 1426, there were rumors that she was going to marry/having an affair with Edmund Beaufort, which is possibly why Parliament passed a law in 1427/28 preventing anyone from marrying a dowager queen without the consent of the king. At this time nobody appears to have made any public connection between the two of them. Sometime after this, Catherine left the king's circle for Hertfordshire, and in 1430 and 1431 she bore Owen Tudor's sons. The public at large had no idea about this relationship until after her death in 1437 (so there was no scandal), but royal insiders probably did, given the pregnancies.

We conclude that they married because after the fact it was accepted as a marriage with legitimate children, and because a woman of her position would have been extremely unlikely to absolutely torpedo her reputation. But we don't know if they married before the law was passed (maybe Catherine was laughing up her sleeve over it) or if they knowingly broke it. Historical chroniclers came up with stories of meet-cutes to give their marriage some extra flavor, but he did not fall into her lap or kiss her when he thought she was a maidservant. However, given that the relationship was secret and ongoing, it's most likely that there was a romantic angle that motivated Catherine to do something that was otherwise entirely against her best interests.

That is, we know almost nothing, or actually nothing, about many individuals' motivations and private feelings in the period. This is particularly true of women. There is no record, as far as I'm aware, of Anne genuinely and privately explaining her choices on this matter, or her feelings about the annulment, for that matter, and so all anyone can do is speculate. We also tend to hold the belief today that everyone constantly wants romance/sex and is unhappy alone, but this isn't really the case. Why should we assume that there must have been some significance to the fact that she didn't remarry?