ILR with extended absence from UK

I have the ILR through marriage, but have been coming and going from the UK due to family illness and studying in another EU country, is there any possibility that they would consider my application? I was thinking about asking for an MP to help as well.

No. You will need to be within the absence limits to apply for British citizenship. A local MP has no power to persuade HO to consider your application.

Unless you provide more detail (dates) of your absences etc, more accurate advice cannot be given.