Software Transactional Memory (STM) is an optimistic concurrency control mechanism that simplifies the development of parallel programs. Still, the interest of STM has not yet been demonstrated for reactive applications that require bounded response time for some of their operations. We propose to support such applications by allowing the developer to annotate some transaction blocks with deadlines. Based on previous execution statistics, we adjust the transaction execution strategy by decreasing the level of optimism as the deadlines near through two modes of conservative execution, without overly limiting the progress of concurrent transactions. Our implementation comprises a STM extension for gathering statistics and implementing the execution mode strategies. We have also extended the Linux scheduler to disable preemption or migration of threads that are executing transactions with deadlines. Our experimental evaluation shows that our approach significantly improves the chance of a transaction meeting its deadline when its progress is hampered by conflicts.