Resolving the accretion disks and broad-line regions of active galactic nuclei (AGNs) can probe the physics behind supermassive black hole (SMBH) fueling and weigh SMBHs. With time-domain observations, the reverberation mapping (RM) technique measures time delays between different light curves, probing the AGN inner structures that are otherwise often too compact to resolve spatially with current facilities. Theoretically, the SMBH accretion disk structure does not evolve over decades. Here we report the significant variations in the continuum time delays of NGC 4151. In the high-flux state, our high-cadence (∼2 days) spectroscopy reveals that continuum time delays are $3.{8}_{-1.0}^{+1.8}$ times larger than those in the low-flux state and 14.9 ± 2.0 times longer than the classical standard thin-disk prediction. Notably, the continuum time delays can be comparable to the time delay between Hβ and the 5100 Å continuum, and the latter is commonly used to calculate the BLR sizes. Hence, the BLR sizes are underestimated if the continuum time delays are not considered, which introduces ∼0.3 dex systematic uncertainties on RM SMBH masses. Our findings underscore that simultaneous continuum and BLR RMs are vital for better deciphering the SMBH accretion and mass function.