Hi Lorna,
There are significant advantages in splitting your Levemir dose in my opinion.
Novo Nordisk themselves say that Levemir's action can be over within 18 hours in some people. There seems to be a fairly wide range of activity periods depending on the individual and the size of the dose, but it's pretty unusual to find it working for precisely 24 hours in someone.
One common experience with people taking a single dose is that, because it is larger, it can push blood glucose levels too low overnight and first thing in the morning. Then, as it wears off through the day, blood glucose levels rise the following evening. Both of these things used to happen to me, but simply splitting the dose put an end to them immediately.
Also, as split doses will be smaller, they are absorbed better and less likely to cause swelling or bruising at your injection sites.
All the best,
fergus