remain verb
- linking verb to continue to be something; to be still
in the same state or condition
- to remain standing/seated/motionless
- to remain calm/confident
- Train fares are likely to remain unchanged.
oxford learns dictionary remian
maintain verb
- maintain something to make something continue at the
same level, standard, etc.
- to maintain law and order/standards/a balance/control
- ANU has maintained its position as Australia's top university.
- The two countries have always maintained close relations.
oxford learners dictionary maintain
Maintain is an active verb you have to do stuff to maintain the status quo
Remain is a passive verb it describes almost not doing anything,
remain seated
requires you NOT to stand up
So to your examples:
This research shows that Christmas remains a time of generous charitable giving.
NOTHING has changed nothing has happened Christmas is still a time of generous charity
Stephen Dunmore, the CEO of the Fundraising Regulator, which maintains standards for charitable fundraising ...
The fundraising regulator puts effort into (maintains) ensuring the standards for charities remain (stay the same) high and doing the jobs the charities were designed to do. I.e. the dogs trust spends it's money looking after dogs not sending the board on cruises and expensive nights out.
Last thought
I am not actually sure why "remain" is a verb it is almost like it is a verb because it didn't neatly fit anywhere else. I am going to ask this as my own question. So I got an answer Why is remain a verb