What do do with cases of cross-loading on Factor Analysis?

I have around 180 responses to 56 questions. Each respondent was asked to rate each question on the sale of -1 to 7. This is based on Schwartz (1992) Theory and I decided to keep it the same.

I used Principal Components as the method, and Oblique (Promax) Rotation. I had to modify iterations for Convergence from 25 to 29 to get rotations.

Looking at the Pattern Matrix Table (on SPSS). I noted that there are some cross loading taking place between different factors/ components. These are greater than 0.3 in some instances and sometimes even two factors or more have similar values of around 0.5 or so.

What do I do in this case? Do I remove such variables all together to see how this affects the results? My initial attempt showed there was not much change and the number of factors remained the same.

To clarify, as I have 56 variables, I am trying to reduce this to underlying constructs to help me better understand my results. Using Factor Analysis I got 15 Factors with with 66.2% cumulative variance.