Considering all the clues given, I'd say the answer is..
Jason, as in Jason and the Argonauts
Jason is a greek mythical hero, and following Clue 3, the Roman refine is a calendar (Julian and later Gregorian). The first letters of the calendar months in English are JFMAMJJASOND. So Jason is trapped in time, preceded by mother (MA = March-April), circling around (every year), and will never be free, since it's surrounded by the other months.
Trapped in time by roman refine. = clock hands inside of the numbers which are depicted as roman numerals? Mother precedes we'll never be freed = the minute hand goes around faster than the hour hand so precedes it. They keep going round and so never leave that area. Circling around waiting to be found = as above.
Odyssesus on the island of Ogygia?
A Greek trapped in time refers to Odysseus being trapped on Ogygia by Calypso's singing for seven years. circling around waiting to be found perhaps by my shipmates if they've not met their fates refers to how Odysseus got there. He was shipwrecked and all his shipmates drowned but he washed up on Ogygia.
Google translate tells me that 'the' translated into Greek is 'O' (I am not sure how much to believe this...). Using this as an equivalent to 'a', I 'trapped' it in the word 'ONE' (a time of day) to get 'OONE'.
...by a Roman refine
The Romans are renowned for their road-building. Using the common abbreviation 'RD' for 'road' and further 'trapping' the 'OONE' within we get 'ROONED'.
Add 'MA' (short for 'mother') in front to get 'MAROONED'.
we'll never be freed
You're trapped! Marooned on a desert island! The second stanza's waiting to be found perhaps by my shipmates also implies this...
I can't account for the first two lines, except to say that Odysseus is a Greek who is cursed to travel for a long time. However, the rest of the riddle lines up very neatly. In Book 11 of the Odyssey, Odysseus visits his mother in the Underworld. This immediately precedes Book 12 in which he passes between Scylla and Charybdis at the Strait of Messina.
At first, the ship passes through the Strait by steering close to Scylla, sacrificing some of the men to get the ship through. However, the ship is destroyed in a storm almost immediately afterwards and Odysseus floats back into the Strait on a piece of the ship's hull. This time, he is caught by Charybdis, who creates a giant whirlpool by swallowing the sea. Odysseus escapes by grabbing the branch of a fig tree that overhangs the Strait. Thus, he has to wait while the sea circles around beneath him. He does not know if any of his shipmates survived, but he may hope that some of them did and will come to rescue him. This is not the case, and eventually Charybdis spits the sea, and our hero's raft, back out and he makes his escape alone.