Is the real purchasing power of EBT (and other welfare) being rapidly destroyed by high food inflation?
I will focus on the most recent increase in food price inflation, as analyzing long term trends and/or other benefits would make the question considerably more complicated.
As of June 2020, the annual rate of food price inflation in the US hit 4.5%, the highest it has been since late 2011, according to Trading Economics.
Back in April, monthly benefits were increased 40% according to the USDA.
At least as long as these increased benefit levels remain in place, I think it's probably safe to say no, food inflation has not significantly eroded the real purchasing power of EBT benefits over recent months. However, it may not necessarily be the case that overall food insecurity has declined, taking increased unemployment and other factors in to account. In April, before the increase in benefits took effect, there were signs of greater overall food insecurity, and especially for children according to a piece from the Brookings Institution.
EDIT: @MarkI has pointed out in the comments that this benefit expansion was allowed to expire recently. It was only in place for three months. There are cost of living adjustments made on an annual basis to SNAP as the other answer explains.
The amount of benefit received from the Supplemental Nutrition Assistance Program (the formal name of food stamps) is based on income, size of household, and the cost of feeding a household.
The Secretary of Agriculture is required, every five years starting in 2022, to update estimates of the cost of feeding households of various sizes (7 USC § 2012(u)). The result of this estimate would be used to determine the amount of benefit a household would receive.
While inflation would reduce the buying power slightly over that five-year period, it would be subsequently replenished at the start of the next.