The answer to this is in your contract. How are you contracted with the customer? If time & materials, the customer pays. If cost plus fixed fee, the customer pays but you pay too in terms of your fee margin. If fixed fee, you pay.
Not only do you need to understand the payment terms, but also assumptions and exclusions agreed to in the contract. If fixed fee, there might be a stop loss clause that enables you to go back to the customer if more money to cover these bugs, as an example. If the customer had a Not to Exceed clause in there, you may have had some reporting requirements prior to hitting that ceiling that, if not met, would put YOU on the hook to recover from. If met, then you have good cause to ask for more money.
I am not a contracts expert by any stretch so my examples above are high level. You need to consult with the contracts expert, i.e. legal, to comb through your contract with customer to build a case for more funding OR accept the hit to your profit OR something in between. In addition, I would expect you want to maintain good relations with your customer so you need to consider that, as well, as you comb through your T&Cs of the contract.