They are still in business because they went to the agencies that regulate them and sought exemptions and waivers from the requirements that they not have criminal convictions.
Certain highly regulated industries, like the banking and securities (stocks, bonds, etc.) industries require the companies, their executives, and individual people be licensed. Usually, individuals and companies with a history of "bad behavior", are denied licensure. Each industries regulations and laws define what that bad behavior is, but a felony conviction for a financial related crime certainly meets that definition. However, being denied a license or booted from the industry is not automatic. The agencies that enforce these regulations, have the ability to continue to license someone who has a felony conviction.
I know I am speaking in general terms, but let us look at the securities industry for a specific example.
Under the Investment Company Act of 1940, companies that manage investments/mutual funds, like J.P. Morgan & Chase, Co. must be licensed by the Securities and Exchange Commission. To paraphrase, Section 9(a) of the 1940 Act, it says that individuals cannot control or manage an investment company if they had a felony conviction on the past 10 years. It goes on to state that those same requirements apply to companies meaning they are denied a license.
But, section 9(c) allows “people” (which includes companies) that are prohibited from being licensed to get an exemption from these rules through the SEC's administrative process.
Here, JP Morgan and the other companies mentioned in the press release are big players in the securities industry. All of them manage mutual funds and buy/sell securities for clients. Therefore, they each applied and received this exemption at the same time or right before they pleaded guilty so it wouldn’t disrupt their business. Here are the administrative orders from the SEC’s website dealing with this exact issue.
If you’re interested in the law that applies, these orders are a good place to start.
Also, here is a less detailed article on this issue in the NY Times.