stay determined/persistent/persevering

[angliholic]

Studies have found that at least 40% of people break their resolutions after two months! However, if people stay determined/persistent/persevering, the new year can be a new positive beginning.
Do all of the bolded words fit in the above and mean about the same? Thanks.

[Tdol]

I would not use the last two in this way. They would work better as verbs: if people persevere, persist...

[joham]

Dictionaries say 'stay open/ awake/ calm/ quiet/ warm/ cold/ cool'. It seems 'stay' is usually followed by some very short adjectives. Am I right? And what about 'remain'? Can we say 'remain persistent'?
Thank you very much!

[Tdol]

It seems redundant to me to 'remain persistent', as persisting involves not giving up.