Background: Epidermal growth factor receptor-mutated (EGFR+) non-small-cell lung cancer (NSCLC) patients failing tyrosine kinase inhibitors (TKI) can benefit from next-line targeted therapies, but implementation is challenging. Methods: EGFR+ NSCLC patients treated with first/second-generation (1G/2G) TKI at our institution with a last follow-up after osimertinib approval (February 2016), were analyzed retrospectively, and the results compared with published data under osimertinib. Results: A total of 207 patients received erlotinib (37%), gefitinib (16%) or afatinib (47%). The median age was 66 years, with a predominance of female (70%), never/light-smokers (69%). T790M testing was performed in 174/202 progressive cases (86%), positive in 93/174 (53%), and followed by osimertinib in 87/93 (94%). Among the 135 deceased patients, 94 (70%) received subsequent systemic treatment (43% chemotherapy, 39% osimertinib), while 30% died without, either before (4%) or after progression, due to rapid clinical deterioration (22%), patient refusal of further therapy (2%), or severe competing illness (2%). Lack of subsequent treatment was significantly (4.5x, p < 0.001) associated with lack of T790M testing, whose most frequent cause (in approximately 50% of cases) was also rapid clinical decline. Among the 127 consecutive patients with failure of 1G/2G TKI started after November 2015, 47 (37%) received osimertinib, with a median overall survival of 36 months versus 24 and 21 months for patients with alternative and no subsequent therapies (p = 0.003). Conclusion: Osimertinib after 1G/2G TKI failure prolongs survival, but approximately 15% and 30% of patients forego molecular retesting and subsequent treatment, respectively, mainly due to rapid clinical deterioration. This is an important remediable obstacle to sequential TKI treatment for EGFR+ NSCLC. It pertains also to other actionable resistance mechanisms emerging under 1G/2G inhibitors or osimertinib, whose rate for lack of next-line therapy is similar (approximately 35% in the FLAURA/AURA3 trials), and highlights the need for closer monitoring alongside broader profiling of TKI-treated EGFR+ NSCLC in the future.