Purpose: Suicidal thoughts and behaviors have been on the rise in the recent years in the US. There is a well-known link between heavy alcohol use/alcohol use disorders (AUDs) and suicidal thoughts and behaviors. An increase in the respective risk relationships is one way in which heavy alcohol use/AUDs may be driving the increase in the rate of suicidal thoughts and behaviors. The objective of the current study was to investigate whether the gender-specific risk relationships between heavy alcohol use/AUDs and past-year (1) suicidal thoughts and (2) attempted suicide have increased over time. Methods: Individual-level annual data from the National Survey on Drug Use and Health for the past 12 years (2008–2019) were utilized. Year- and gender-specific multivariate binary logistic regression analyses were first conducted. Gender-stratified random-effects meta-regressions across study years were then conducted. Results: Heavy alcohol use/AUDs were associated with elevated odds of past-year suicidal thoughts and attempted suicide for both men and women; however, a linear increase in the risk relationships over time was not found. Conclusion: Although a temporal increase in the risk relationships of interest was not found, until additional research in this area is conducted, heavy alcohol use/AUDs cannot be ruled out as being a driving force behind the increasing rate of suicidal thoughts and behaviors in the US.