Regression testing aims to prevent code changes from breaking existing features. Flaky tests negatively affect regression testing because they result in test failures that are not necessarily caused by code changes, thus providing an ambiguous signal. Test timeouts are one contributing factor to such flaky test failures. With the goal of reducing test flakiness in SAP HANA, we empirically study the impact of test timeouts on flakiness in system tests. We evaluate different approaches to automatically adjust timeout values, assessing their suitability for reducing execution time costs and improving build turnaround times. We collect metadata on SAP HANA's test executions by repeatedly executing tests on the same code revision over a period of six months. We analyze the test flakiness rate, investigate the evolution of test timeout values, and evaluate different approaches for optimizing timeout values. The test flakiness rate ranges from 49% to 70%, depending on the number of repeated test executions. Test timeouts account for 70% of flaky test failures. Developers typically react to flaky timeouts by manually increasing timeout values or splitting long-running tests. However, manually adjusting timeout values is a tedious task. Our approach for timeout optimization reduces timeout-related flaky failures by 80% and reduces the overall median timeout value by 25%, i.e., blocked tests are identified faster. Test timeouts are a major contributing factor to flakiness in system tests. It is challenging for developers to effectively mitigate this problem manually. Our technique for optimizing timeout values reduces flaky failures while minimizing test costs. Practitioners working on large-scale industrial software systems can use our findings to increase the effectiveness of their system tests while reducing the burden on developers to manually maintain appropriate timeout values.