Predicting the default of small and medium-sized businesses (SMEs) using the hazard model approach represents an area relatively neglected by mainstream literature. On the one hand, SMEs are regarded as the backbone of the economy; on the other hand, their specific features pose a challenge to the modelling process. This issue is further complicated by the fact that many modern structural approaches to default modelling are simply unsuitable for SMEs due to their limited size. Therefore, researchers only rely on accounting, non-financial, or macroeconomic data. The gap is especially noticeable in several studies on SME default prediction that employ the hazard model approach, which models the probability of default with respect to the time factor. A better understanding of the factors driving SMEs’ default might help in adopting policies that strengthen their competitiveness. The aim of this study is to introduce a hazard model for EU-28 SMEs and analyse the contribution of macroeconomic indicators and proxies of external financial obstacle factors. This model was derived using the Cox semiparametric proportional model, leaving the baseline hazard unspecified and employing macroeconomic variables as explanatory variables. By analysing a sample of 202,209 European SMEs over the period 2014–2019, the results indicated that factors of employment rate, personal cost per employee, and interest rate play significant roles in determining the survival of SMEs. Adding these macroeconomic variables significantly increased the area under curve values compared to the situation where only accounting variables were used.