I used to be on Lantus, before that it was Mixtard and Humilin I. When I swapped onto Lantus, initially my sugar levels improved, but I didn't feel that it was working as effectively. So I was swapped on to Levemir twice a day. Over the past few years, my doseage has gone up (now 32 units each dose).
So for me, it was normal to increase the dose. However, I think it does depend on the individual, everyone's body is different, I didn't react well to Lantus for instance, but I know people that didn't get on with Levemir.
Contact your DSN if you're concerned about your BG Levels increasing despite using Levemir, they would be able to advise on what they think could help or what you should use. The important thing is to keep testing every couple of hours for a few days and see if you can spot any patterns with your levels that could explain what the Levemir is doing.