At a time when the home side occupy 17th position in the standings, Bristol City have been on the opposite trajectory and sit in 13th spot.
Match preview
There has been a common theme with Swansea's most recent results, the Welsh outfit succumbing to defeat and Martin insisting afterwards that his team deserved more.
While that may ring true to a certain extent, Swansea have now won just three of their last 21 fixtures in the second tier, losing seven times in their most recent nine outings.
Still eight points clear of the relegation zone after facing three promotion contenders in a row, Swansea will likely have enough to avoid relegation, yet it should not be lost that they could have pushed for promotion at one stage.
As it stands, it is unclear whether a mutual parting ways of the way is the inevitability that it seems, but Martin will feel that there is still potential for this team to improve.
With showdowns against Bristol City and rivals Cardiff City to come either side of the international break, he will recognise that his long-term future may hinge on those two fixtures.
Bristol City have already travelled to Swansea this campaign, prevailing 2-1 after extra time in an FA Cup tie as recently as January 17.
However, despite making the fifth round of that competition, it has been the Robins' form in the Championship which has caught the eye with 20 points coming from 12 matches since the turn of the year.
Although just 10 goals have been conceded in those fixtures, the 1-0 reverse at Luton Town in midweek has left Nigel Pearson's side 12 points adrift of the playoffs.
With just nine matches remaining, Bristol City are now likely out of contention, yet Pearson will be eager to end a run of four away league fixtures without success.
Swansea City Championship form:
L
L
D
L
L
L
Bristol City Championship form:
D
W
L
D
W
L
Bristol City form (all competitions):
W
L
L
D
W
L
Team News
Swansea are still missing Jay Fulton and Joel Latibeaudiere, who serve the second game of their two-match suspension for 10 yellow cards.
While much of the team from the Millwall fixture will likely remain the same, Oliver Cooper is back in contention after a knock and could start.
With Liam Walsh expected to drop down to the substitutes' bench, Cooper, Morgan Whittaker and Jamie Paterson are all competing for spots in the final third.
Despite a narrow defeat at Luton, Person may be against tinkering with his Bristol City XI.
Amid a number of injuries in defence, Mark Sykes could keep his place at right-back ahead of George Tanner, but Matty James will be in contention to start in midfield if he manages to shake off an ankle injury.
Swansea City possible starting lineup:
Fisher; Darling, Cabango, Wood, Manning; Cundle, Grimes, Ntcham; Cooper, Piroe, Cullen
Bristol City possible starting lineup:
O'Leary; Sykes, Vyner, Pring, Dasilva; Scott, King; Cornick, Weimann, Mehmeti; Wells
We say: Swansea City 1-1 Bristol City
Such is the increasing pressure on Swansea that Bristol City will fancy their chances of inflicting another defeat on their hosts. Nevertheless, even with the Robins in a position where they need to push for maximum points, we expect Swansea to do enough to earn a share of the spoils.