He has recently threatened to resign if the IRA don't begin decommissioning weapons within an agreed deadline. The IRA don't seem inclined to do this.
Combined with the fact that they performed pitifully in the UK General Election 2001 (UUP 6 seats, DUP 5, Sinn Fein 4 and SDLP 3, as I remember), it seems as though Mr. Trimble's political days are numbered.
It was Mr. Trimble who persuaded the unionists that the Good Friday Agreement was A Good Thing, and that it was not simply gving in to the nationalists. It is generally accepted that unionist support for the Good Friday Agreement is dependent on Mr. Trimble's leadership of the UUP; his resignation would exacerbate party splits and give more political opportunity to the rabidly unionist DUP, led by the equally rabid Reverend Ian Paisley. It therefore seems likely that his resignation would lead to the collapse of the Good Friday Agreement, and a return to the 'Troubles'.
And no, there is no good reason why this is softlinked to cat shaving techniques. Casualty of the search button.