In this letter, we consider the sparsity-based time-frequency representation (TFR) of frequency-modulated (FM) signals in the presence of burst missing samples. In the proposed method, three key procedures are used to mitigate the effect of missing samples. First, each slice in the instantaneous autocorrelation function (IAF) corresponding to the time or lag domain is converted to a Hankel matrix, and whose missing entries are recovered via the atomic norm-based approach. Second, a signal-adaptive time-frequency kernel is used to mitigate the undesired cross terms and the residual artifacts due to missing samples. Third, we apply a rank deduction technique on the obtained IAF to provide reliable TFR reconstruction results.