Donald Tusk, president of the European Council, wrote: "EU leaders agree to move on to the second phase of #Brexit talks. Congratulations PM @theresa_may."As May headed home from Belgium on Thursday night, she would have been confident that her terrible year was about to end on a positive note. This would be some achievement after a 2017 in which she lost her government's majority in an election she didn't need to call and when Brexit talks seemed to be forever stuck at first base.May had just been applauded by fellow European leaders at a dinner designed to back the deal on the first stage of the UK's withdrawal from the European Union. The dinner was a prelude to the formal approval of the deal Friday by the remaining 27 EU countries — agreeing on Britain's proposed financial settlement with the bloc, a tentative arrangement on the future of the border between Ireland and Northern Ireland, and the rights of European citizens living in the UK.As May must know by now, however, a success one day can be overturned the next. Tusk's tweet gives the green light to the next stage — but a lot could still happen in the final days of 2017.However genuine Thursday evening's applause in Brussels might have been for the Prime Minister — and it was "not very enthusiastic," according to Austrian Chancellor Christian Kern — she is increasingly weak at home. On Wednesday evening, lawmakers from her own side defeated May on a key vote on her government's Brexit legislation. A second rebellion on a measure to enshrine in law the date of leaving the EU looms next week — and there have been reports in the British media that May is considering backing down on this, rather than suffering a second defeat. In the last six weeks, the Prime Minister has lost two Cabinet ministers, and an official investigation hangs over a third. These events are unrelated to Brexit but have nevertheless added to the sense of crisis in Downing Street.For May, the deal approved Friday was hard-fought and hard-won. It almost fell apart earlier this month when Arlene Foster, the leader of the Democratic Unionist Party in Northern Ireland on whom May's Conservative government relies on for a working majority in the British Parliament, withdrew support for a draft that would have seen Northern Ireland be subject to different customs arrangements than the rest of the UK. Frantic phone calls between the two women averted a disaster, and a new deal was struck a week ago.After six months of wrangling over the first phase of negotiations, not helped by conflicting comments from May's Brexit minister, David Davis, getting this deal is a real achievement. Yet this is only phase one: The more contentious issues will arise in the next one when Britain and the EU wrangle over post-Brexit trading arrangements. Talks on how long the transition period — designed to avoid a cliff edge for British businesses after Brexit happens — could begin as early as next week, and then discussions over trade will likely start in March. Yet not even May's Cabinet is in agreement on what a British-EU trade deal should look like, so the mood on both sides of the channel is far from jubilant.As Jean-Claude Juncker, president of the European Commission, said Friday morning: "The second phase will be significantly harder than the first and the first was very difficult." Whether Brexit will happen "depends on the British Parliament and British people."In a sign that EU leaders have finally reached the business end of Brexit negotiations, May held informal talks over apéritifs with key European power brokers — German Chancellor Angela Merkel and French President Emmanuel Macron — before the formal dinner began Thursday evening. Merkel sounded a note of caution Friday morning, saying there was "much more work to be done and time is of the essence."The year may end on a high for the Prime Minister, but there are plenty more hurdles for her to jump over in 2018. She knows it, her colleagues — and opponents — in the UK know it and crucially, so do her European counterparts.