Based on your information:

Firstly, To run a logistic regression for 20 variables at a time, your sample size is not enough.

Secondly, start with binomial logistic regression for all variables individually, then which ever is significant or near significant. Take those variable into your final model.

There are different type of regression model you can try else

Like forward, backward, or stepwise etc.

Lastly, here is a brief About Co-variance matrix:

"There are two concepts inherent in a covariance matrix–covariance and matrix.  Either one can throw you off.

Let’s start with matrix.  If you never took linear algebra, the idea of matrices can be frightening.  (And if you still are in school, I highly recommend you take it.  Highly).  And there are a lot of very complicated, mathematical things you can do with matrices.

But you, a researcher, don’t need to be able to do all those complicated processes to your matrices.  You do need to understand what a matrix is, be able to follow the notation, and understand a few simple matrix processes, like multiplication of a matrix by a constant.

The thing to keep in mind when it all gets overwhelming is a matrix is just a table.  That’s it.

A Covariance Matrix, like many matrices used in statistics, is symmetric.  That means that the table has the same headings across the top as it does along the side.

First, we have substituted the correlation values with covariances.

Covariance is just an unstandardized version of correlation. 

To compute any correlation, we divide the covariance by the standard deviation of both variables to remove units of measurement.  So a covariance is just a correlation measured in the units of the original variables.

Covariance, unlike  correlation, is not constrained to being between -1 and 1. But the sign will always be the same, and a covariance=0 has the exact same meaning as a correlation=0–no linear relationship."(1)

1. https://www.theanalysisfactor.com/covariance-matrices/

The covariate matrix (and not the covariance matrix) is the matrix that contains a column of reach variable in your data set and a line for each observation.

If it cannot be computed, it means that something unexpected occurs with your data. The most probable explanation is that some values are missing in your data; the software then tries to consider only patients with complete cases. But it may well be that there is no such patient (that is, no patient without any missing data), so the covariate matrix cannot be computed. Which means that you must first deal with your missing data.

I guess other explanations may also hold, like unrecognized data types or corrupted data file, but I would first check this missingness pattern.

Thank you very much Mehul Kumar Chourasia for your comprehensive comments

Regards