Fisher Scoring Algorithm did not converge however model output looks fine in R

Question

I am currently trying to fit a logistic regression model in R with separated data to analyse the problems occuring in such a case. Indeed for the following model warning messages occured, however in the model summary the standard errors and coefficients do not indicate any major issues in my opinion, and the number of fisher scorings is also not above 25, but rather low (= 2). Does anyone of you have ideas, why this could be the case? I have already checked that the data is indeed separated.

Code:
lr_master_ECTS_sem <- glm(glm(cod_master_SJ_bin ~ am_ECTS_total + semester, data = data, family = binomial(link = "logit"))
)

Output:
Call:
glm(formula = glm(cod_master_SJ_bin ~ am_ECTS_total + semester, 
    data = data, family = binomial(link = "logit")))

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -0.5920092  0.0982783  -6.024 2.31e-07 ***
am_ECTS_total  0.0036223  0.0007227   5.012 7.74e-06 ***
semester       0.0442304  0.0123937   3.569 0.000826 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 0.06791891)

    Null deviance: 8.6275  on 50  degrees of freedom
Residual deviance: 3.2601  on 48  degrees of freedom
AIC: 12.478

Number of Fisher Scoring iterations: 2


Warning messages:
1: glm.fit: Algorithmus konvergierte nicht (did not converge)
2: glm.fit: Angepasste Wahrscheinlichkeiten mit numerischem Wert 0 oder 1 aufgetreten (probabilities with values of 0 or 1)
3: glm.fit: Algorithmus konvergierte nicht 
4: glm.fit: Angepasste Wahrscheinlichkeiten mit numerischem Wert 0 oder 1 aufgetreten 

UPDATE:

 ### standardized
> # Standardize the regressors using scale()
> data_standardized <- data
> data_standardized$am_ECTS_total <- scale(data$am_ECTS_total)
> data_standardized$semester <- scale(data$semester)
> 
> # Fit the logistic regression model with standardized regressors
> lr_master_ECTS_sem_standardized <- glm(cod_master_SJ_bin ~ am_ECTS_total + semester, data = data_standardized, family = binomial(link = "logit"))
Warning messages:
1: glm.fit: Algorithmus konvergierte nicht 
2: glm.fit: Angepasste Wahrscheinlichkeiten mit numerischem Wert 0 oder 1 aufgetreten 
> 
> # Summary of the model with standardized regressors
> summary(lr_master_ECTS_sem_standardized)

Call:
glm(formula = cod_master_SJ_bin ~ am_ECTS_total + semester, family = binomial(link = "logit"), 
    data = data_standardized)

Coefficients:
              Estimate Std. Error z value Pr(>|z|)
(Intercept)    -104.07   48318.32  -0.002    0.998
am_ECTS_total    82.96   62815.32   0.001    0.999
semester         97.21   68864.96   0.001    0.999

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 5.3182e+01  on 50  degrees of freedom
Residual deviance: 8.8010e-09  on 48  degrees of freedom
AIC: 6

Number of Fisher Scoring iterations: 25

Standardizing did indeed reveal the problematic model structure.

Answer 1

Your model output is not fine unfortunately. Judging by the fact that, after standardizing the predictors, the intercept is taken to be -100 on the log odds scale, you just don't have enough events to fit a logistic with 2 covariates. I already see you have just 50 observations, so I would guess maybe the number of events is 10 or fewer, and the size of the effect is large. I would guess therefore, that the covariates are strongly stratifying, and all negative and positive cases lie below and above some combination of covariate values, respectively. This is separation. As a result the odds ratio tends to explode off into infinity, and the model results can't be trusted. Without standardizing, the fitter terminates early and gives an unreliable estimate of inference which suggests statistical significance, with standardizing the opposite is true although the log odds ratios are much larger. Normally standardizing covariates would not affect the overall inference on their values (putting the issue of interactions aside), but the fact that these are different portray the issue of modeling singularity.