Gloucester resumed on 36-0, some 156 runs short of a total which would force Warwicks to bat again.
Kabir Ali was the first player to lose his wicket,being caught by Frost off the bowling of Chris Woakes with the score on 47. Eight runs later, and Warwicks took another wicket. This time it was Porterfield who went caught by Jon Trott.
Another five runs later and Warwicks were sensing an innings victory when Taylor was dismissed for one run from seven balls.
However, Marshall and Snell turned the game back into the favour of the visitors after a break for rain, with a stand of 103 before the former became Chris Woakes second victim.
Gloucestershire made 26 more runs before the rain came down for a second time and the game, umpired by former football referee Martin Bodenham ended as a draw.
Warwickshire's next fixture is the Twenty/20 Quarter-Final v Kent Spitfires on July 9th AT 5.40pm, followed by a tour match against Bangladesh A at Edgbaston from July 11-13