Is it correct to find that an explanatory variable was found to be statistically significant with the chi-square test but insignificant with the logistic regression analysis model?
Cleared up and partially answered in comments:
This logistic regression model has several explanatory variables, about 10 of them. – Etta
It sounds as if you are running the risk of double dipping. You can't use associations with Y to decide which variables to test for associations with Y. Besides that, adjusted and unadjusted (for covariates) analyses naturally differ. – Frank Harrell
Does this mean that the results might be faulty or the approach wrong? – Etta
Correct. Look at some of the rules of thumb for the required sample size as a function of the number of candidate predictors, and pre-specify a full model and use it as the basis for your conclusions. – Frank Harrell