For a federally tax-exempt nonprofit, there is no limit on the amount a nonprofit can maintain in its treasury. Unlike a business which could at least theoretically be taxed on excess reserves, the Tax Code provides neither limits nor tax on the amount.

We are not aware of any state limitations on the amount, so long as the funds are used for the purpose of the organization.

A huge surplus may make it more difficult to raise funds, but remember that Harvard University had an endowment of more than $30 billion in 2013 and they seem to convince donors to give more each year.

UPDATE 1/24;

The market value of Harvard's endowment dropped to $50.7 billion as of June 30, 2023, down from a peak of about $53 billion on June 30, 2021.  In the 2017 tax bill, Congress imposed a new excise tax of 1.4% on net investment income on a small  group of private universities that have endowments valued at more than $500,000 per full time student.  (See Ready Reference Page: "Tax Bill Not God for Nonprofits, But Not as Bad As It Might Have Been.") The IRS reported that it collected $243 million in taxes on 58 such institutions in 2022.