Hashem hardened Pharaoh's heart so that he would not do teshuva and release the Bnei Yisrael. This is stated several times. In Shemos see 3:19, ואני ידעתי כי לא יתן אתכם מלך מצרים להלך ולא ביד חזקה, in Va'eira see 7:3 ואני אקשה את לב פרעה, and in Bo, 11:1, כי אני הכבדתי את לבו. From the emphasis and the repeated explanation that it was Hashem's desire to show the world how mighty Egypt would be like a plaything to Hashem, one might think that this was a singularity, a event exclusive to that one place and time. It is not. The ability to do Teshuva has been taken away from other people as well and continues to be a possibility.
I don't mean to provide excuses for people that want to fool themselves into thinking they can't do teshuva. This only happens to highly accomplished resha'im. If you're not a world-class achiever in something else, you probably aren't a world-class Rasha either. To emphasize this, here is something from the Brisker Rov, (quoted by Rav Shlomo Wahrman, author of שארית יוסף and Rosh Yeshiva of Hebrew Academy of Nassau County,) in HaPardes year Year 62 number 1, 1987, to the effect that even an Amaleiki can do teshuva.
Then, Reb Yisrael Salanter:
Finally, I found it interesting that several Achronim (the Nesivos, Rav Bergman, and several others, with approximately the same approach) use this idea to explain the discussion between Reb Meir and Bruria in Brachos 10a. Reb Meir held that since they were beyond teshuva, there was no point in their living, and they would be better off dead, to avoid further sins, and the world would be better without them. Bruria taineh'd that the inability, or the loss of siyata dishmaya to do teshuva is an onesh, and for onshim you can be mispallel. So she told Reb Meir to daven that their onesh of "no access to Teshuva" should be removed, and then maybe they could be mashpia on them to do teshuva. Or it could be they were arguing about whether they were on level two or three of Reb Yisrael Salanter's chart. Neither pshat, I'm sorry to say, clicks in the words of Reb Meir or Bruria. Also, I find it hard to believe that Reb Meir had any way of knowing that they were already on the madreiga of Ein Maspikin, because then the Tzadikim of Yerushalayim who weren't mochi'ach the resha'im (Shabbos 55a) would have the same excuse. There are those that want to support this pshat by saying that Reb Meir recognized the syndrome from the fact that all his efforts to be mekareiv them, and their being unaffected by the proximity of such an Adam Gadol, so it must be that they are beyond hope. Sorry, not convinced. But it's a nice pshat anyway, because even if it's not a valid interpretation of the conversation between Reb Meir and Bruria, the idea that even a person from whom Teshuva has been taken away has hope, the hope that through Tefilla his access to Teshuva will be restored.
NOTE: in the comments, Reb Micha Berger presents a formidable argument to the effect that it is incorrect to characterize the Kappara of Teshuva as being l'maala miderech hateva. Please see there, where I cite Rabbeinu Bachay and the Shla'h (partially cited in the notes in the Kad Hakemach and more fully in my comment) and Reb Micha's response and citations.
Reb Micha has since posted on this question at his Aish Das website, writing, as always, with serious thought and care.
On that topic, here's a nice video about the human ability to change.