If you've been beating the meringue for a long time and it refuses to reach the stiff peak stage the most likely reason is that a spot of egg yolk accidentally made its way into the bowl. Even the smallest amount will prevent the whites from whipping up and sadly, there is no way to rectify this issue other than starting again. Likewise, any grease in the bowl will have the same effect. For this reason, ensure your bowl and beaters are perfectly clean before starting.