Businesses renegotiate contracts all the time, for many reasons, and the attempt to renegotiate a contract is both a) not a refusal to honor the original contract and b) not a thing you should, in general, be particularly offended by.
People have rather good intuitions for this when they're e.g. asking a bank CSR to waive an overdraft fee but they do not necessarily have the same intuitions when e.g. a client says "So, that money you think I owe you: can I pay you less than that, and later than you want it?"
And indeed there are some circumstances where you *should happily agree* to a renegotiation against your narrow interests!
"That sounds implausible."

If you're a B2B SaaS, and a client either says cashflow issues or is transparently hitting all their vendors and asking to trade in their good customer brownie points for money, there is a really simple calculation in good times or bad.
a) If I give the customer a month free, I am out either COGS for one month or revenue for one month depending on boring specifics. Upside: potentially account doesn't churn.

b) If I don't, very high likelihood that they pay what they owe and churn immediately.
So if you valued goodwill at literally zero—this isn't a relationship it is a vending machine—then this is strictly a math problem and under most plausible assumptions the answer to the math problem is "Comp them a month, put a note on the account, done in ~3 minutes."
n.b. If you're a well-operated B2B SaaS company you long since have given your front-line CSRs the ability to authorize this accommodation on their own authority up to $X00 (minimally) because this is such a screamingly obvious call that it isn't worth Finance or management time.
When I ran a SaaS company the standard language was approximately:

"No worries, we're a small business too and know times can sometimes be tough. I've told the accountant to write off the X invoice in consideration of you being a good client. Best of luck and skill."

I don't actually have to get the accountant's approval for business decisions, and technically the interaction was "I pushed a button and it does what the accountant would expect it to do without paying him $600 an hour to examine a communication."
And mentioning the "small business" part is not accidental, because I know you probably have a boss who has asked you to shake down all the vendors, and I expect you go back next month and say "I just wouldn't feel right doing it again."
"What do you do if they refuse to pay next month?"

Mostly they don't; they slow roll invoices and a SaaS company leisurely attempts to convert invoices to money.

If they outright refuse to pay, cool, businesses gonna business. Really clear no regret decision at that point.
I recall one customer (a used car dealership, not shockingly) who disagreed that they had actually signed up for our service, refused to pay for 6 months of services, then demanded a 50% discount going forward because we were overpriced.

They seemed... surprised to hear "No."
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