1st you must read and follow the defined test method for the voltage rating and ensure you have high quality parts that meet spec. otherwise if either is not true , you have no margin or failure. Cap reliability depends on margins and are better from "name-brand" high quality Japanese companies and less likely from Chinese low cost parts where you can expect these anomalies.
When ESL is not a factor with prober test probing, you can expect Ceramic ESR*C=T values in the range of 0.1ps to <100ns depending on size and thus short circuit current Isc, will be defined as Imax=V/ESR when scope bandwidth is not a limitation.
e.g. 10nf in a low ESR X7R 603 ( COG is lower ESR*C but also small max C) I might expect
The DC breakdown voltage (BDV) can below than the DC BDV which is due to an effect called the double-layer capacitance (memory effect known in all ceramic materials except COG/NP0) where near rated voltage a partial discharge, PD can occur in ANY dielectric including air, if there even just a trace amount of mobile ions or contaminants hard to eliminate completely. When these ions detonate between particles of insulation they arc and drop the voltage across those molecules thus raising the voltage of the balance of the insulation causing more particles to zap resulting in a Relaxation oscillator effect if you current limit the applied voltage.
In a pure vacuum or ultrapure plastic or ceramic part, the PD may be at 99% of the BDV, and with DC applied and current limited, the PD has more time to build up speed under the high E field forces and if DC is not current limited then the follow-on DC current can destroy and blow up the cap. But IF current limited to low energy, only burns some particles inside. PU and some PE plastic caps are known to "self-heal" when this occurs even with the grid across the cap, because the particle size is so small the energy only detonates the particle into an insulator again or in some designs by Panasonic using distributed fusing, the defect only is fused open reducing the total capacitance by a small amount.
The bigger the gap and the bigger the Q=CV, the more pico-coulombs of charge get dumped by the PD, when the energy is enough to cause a cascade of events, it will result explosion limited by energy supplied V^2/ESR. Thus ultralow ESR caps like ceramic and e-caps can discharge more energy while plastic tends towards self-healing by design only. Batteries are exactly the same in these characteristics except the ESR,C values are different where capacitance from high dielectric constant, \$\epsilon_r\$, results in >10k Farads from a tiny LiPo cell or AA alkaline but the ESR will limit the energy and conductor faults or insulator faults from excessive contaminants and high temp may also result in explosive venting an hopefully fusing all dependent on the battery energy and ESR.
The rating for the highest quality cap or dielectric ought to have the same BDV for AC and DC as long as the range of voltage stays exceeds the design limits. Polarized caps can have AC current as long as the reverse DC voltage does not exceed 10% for failure and 5% for margin depending on duration.
If you suspect PD before BDV, reduce the ramp rate just below threshold and wait 1 minute or use a slow ramp V ust below threshold.
You should expect 10% margin at least at room temp and perhaps no margin at max rated temp or expect it to degrade in BDV at high temp. So sounds like you either have a test method or quality problem.