To a degree, it depends on the kind of modification plan you are in. Is it a private modification negotiated between you and your servicer or an old Home Affordable Modification Program (HAMP) or FHA modification?
If you are in a private modification, you should contact your servicer when you suspect that you will be having trouble making payments -- the sooner the better. Negotiating a new modification may or may not be possible; please know that the servicer's role is to try to negotiate the most favorable outcome for the owner of the loan, and is not under any legal obligation to offer you new terms and conditions. However, they do need to review your situation and provide clear information about your rights and any appropriate timelines.
If you're in an old FHA-HAMP, that program is still active and you may be able to get a new modification after a trial payment plan period has been successfully completed. The old HAMP program (discontinued 12/31/2016) has been replaced by a new Flex Modification program. According to Fannie Mae's Flex Modification FAQ it is noted that:
Borrowers who previously modified their loan through HAMP (or any of the predecessor programs) are eligible for a Flex Modification IF:
a. the mortgage loan meets all of the eligibility requirements for the Flex Modification Program (including but not limited to the following):
i. The mortgage loan must be delinquent or in imminent default
ii. The mortgage loan must not have been modified three or more times, regardless of the loan modification program
iii. The mortgage loan must not have received a Flex Modification and become 60 days or more delinquent within 12 months of the modification effective date without being reinstated.
iv. The borrower must not have failed a Flex Modification Trial Period Plan within 12 months of being evaluated for eligibility for another Flex Modification.
For details about the program, read Flex Modification: An outline of HAMP's replacement.
To get started, you'll want to contact the servicer of your loan. Look on your mortgage statement for contact phone numbers or website locations; some may have special numbers or site locations for borrowers having trouble with their loans. Talk to them as soon as you can and see what relief they might be able to offer you.
