Angela Merkel has been the leader of her centre-right CDU party for 16 years and chancellor of Germany for more than 10. For most of the last decade she has been beyond question the commanding figure in European politics. But for how long can she go on? In particular, is she the inevitable leader of her party into the next German general election in autumn 2017, when she would be seeking a fourth term as chancellor?

These questions have been lurking in the corridors of power in German politics for many months. But after three regional elections at the weekend, they have taken on new immediacy. The CDU lost vote share in all three regions that voted on Sunday, failing to win two regions where the party had hopes of victory and slipping badly in the third, while remaining in first place. Some of those losses contributed to the rise of the anti-refugee AfD party, which has opposed Mrs Merkel’s liberal approach to refugees. It was, as she said on Monday, a difficult day. With autumn 2017 now not far away, CDU nerves are still jangling.

Yet it would be a premature mistake to assume that Sunday’s results mark the beginning of the end either for Mrs Merkel or even for her policy. For one thing, contrary to some of the more simplistic early readings, these results gave a mixed message to the ruling party. The CDU’s vote declined by 3% in two of the regions, Rhineland-Palatinate and Saxony-Anhalt, and by 12% in Baden-Württemberg. These were obviously not good results, but they could surely have been a lot worse, given both the stage in the political cycle and the passions aroused by migration. Since the local CDU in both Rhineland-Palatinate and Baden-Württemberg had distanced itself from Mrs Merkel’s policy, and since these elections were won by the centre-left SPD and by the Greens respectively (both of which supported a more liberal approach to refugees) it is hard to pin the CDU’s relatively poor showing on the chancellor or her approach to migration.

Mrs Merkel therefore lives to fight another day. The CDU also remains the strongest party in German politics. This is partly because, in spite of the truly spectacular showing by the incumbent Greens under Winfried Kretschmann in what was once the CDU stronghold of Baden-Württemberg, none of the established parties seems yet to be a serious rival to the CDU in the general election when it comes. The SPD and the liberal FDP both marked time or declined at the weekend.

The rise of the anti-refugee AfD – which sits in the same group as the British Conservatives in the European parliament – was clearly the immediate story of these elections. The party went from nowhere to a double-figure share in all three contests, rising to 24% in Saxony-Anhalt, which is part of the poorer and less liberal former east Germany. It mobilised people who had voted in recent elections and it took votes from all the other parties, not just the CDU (indeed one in six AfD votes in Saxony-Anhalt came from the former communist Left party).

It was a spectacular result. But it needs to be interpreted with care and proportion. This is not the rebirth of Nazism. Nor does it mark the end of German openness to migration. The truth is that, with these elections, Germany may now have become a more normal European country than it was before, having resisted that change longer than most of the others. Its big parties are in decline. The old party system is splintering. Germany is now sporting its own anti-immigrant party alongside the others, much as Ukip and the Front National have muscled their way on to the stage in Britain and France.

Mrs Merkel and her migration policy have had a rebuff. But the chancellor is an adaptable leader. When her party first lost to the Greens in Baden-Württemberg five years ago, she did an about-turn on nuclear power and was re-elected stronger than before as chancellor in 2012. In the wake of the Cologne attacks, she was already taking a tougher line on refugees than she did in the summer. These results will confirm her in that caution. They will make her more determined than ever to drive through the provisional deal with Turkey at the EU summit later this week.

Large uncertainties nevertheless remain. Mrs Merkel is weaker than before. She has problems with her party and with EU partners. She still leads the most important country in the EU, but the other players can sense her weakness. Mrs Merkel has been written off before. But the decision she faces about whether to run again in 2017 just got more difficult, not more straightforward.