How do I modify logistic regression in my case (for repeated measures)? I am a physician conducting some research in Critical Care patients (I have full ethical approval, none of my results will be used to inform patient treatment, etc).
When a person's lungs are enormously sick, they can be turned on their front. It often helps.
I have a dataset from around 135 patients who have had this maneuver performed. I am trying to create a logistic regression model (if appropriate) to examine if there are differences in the response of patients who undergo this. My outcome variable is 'death during ICU admission' (yes/no), and I have blood tests from before and after the positioning maneuver was performed. Each patient had between 1-13 of these changes in position performed (in total I have 360 instances of this happening in 135 patients).
As far as I am aware, it is inappropriate for me to perform logistic regression since the 'treatment' was often performed multiple times on each patient.
My question is as follows; do I need to modify my approach to logistic regression to analyze this data? Alternatively, is there a completely different approach I must use to do this?

You are right that it would be inappropriate to use all 360 observations as they were independent. You could run a logistic regression on the 135 first treatments though. Of course this would lose information. There are models for logistic random effects regression that can model dependence within a patient, see for example here: Li et al. (2011) Logistic random effects regression models: a comparison of statistical packages for binary and ordinal outcomes. BMC Medical Research Methodology. However I'm very skeptical about whether these would be appropriate here, because they make very restrictive assumptions about how within patients dependence looks like (the standard random effect just adds a patientwise constant to the linear predictor; I doubt that this is what goes on in your case). I would probably first produce some visualisations in order to have a better idea about how within-patient dependence actually plays out before doing any modelling of it (actually, running a logistic regression with all data points in an exploratory manner for the sake of looking at how fits and residuals depend within-patient but not to be trusted as final result could be worthwhile). Also whatever you do should be informed by prior knowledge about what reasons may lead to performing the treatment several times, and what implications this has regarding all involved variables.
