I'm doing a Bayesian logistic regression $Y \sim X$ where my predictor $X$ is a count observed over time. So $Y$ and $X$ are each $m x n$ matrices where $m$ is the number of subjects and $n$ is the number of observation years. $Y$ is filled with values in $[0,1]$ and values of $X$ are in $[0, 1, 2,\dotsc]$. For a given subject, $X$ is obviously monotonically increasing over time and it's highly autocorrelated.
Is there a problem to regress on such an autocorrelated independent variable? I've read that as soon as errors are not autocorrelated, there is no problem. But in logistic regression there is no error term as I model the mean of the probability of success right? So how can I test for autocorrelated errors if there are no errors?
EDIT: See $Y$ as failures on thousands of systems and I'm trying to give a probability of failure for each of these systems from $X$ which is the cumulative count over the years of minor accidents that happened individually in the past to each of these systems. Presumably, these accidents act like precursors of the future failure. Example: system 1 has a cumulative count of 37 minor accidents and the predicted probability of failure for this system is 1.2%. Lastly, failures can happen more than once on a given system (but I can assume that these individual failures are independent over time).