In clinical trials for chronic heart failure (CHF), time to a composite of first hospitalization for worsening heart failure or death is a widely accepted primary efficacy measure. Motivated by lower event rates in recent CHF trials, there are proposals to use endpoints accounting for recurrent heart failure hospitalization (HFH) events (e.g. recurrent HFH events plus death as an additional event) as the primary endpoint to better quantify disease burden and to improve trial efficiency. However, analysis and interpretation of recurrent event endpoints may be complicated by the terminal event death. In a previous simulation study it was shown that the type I error rate was well-controlled for the analysis of the composite recurrent event endpoint using the negative binomial (NB) model and the Lin-Wei-Yang-Ying (LWYY) model. As these results were based on limited scenarios, we extended the previous simulation study and identified situations where the type I error rate is no longer controlled for the analysis of the composite recurrent event endpoint using the LWYY model, despite a neutral effect on HFH and a detrimental effect on death of the experimental treatment. Therefore, depending on clinical settings, the LWYY model should be applied and interpreted with more caution.