Ally McCoist will feel as though circumstances are conspiring against him, but it is results that are providing the most probing questions about his management.

The four cup competitions alone have been chastening, with only one of seven ties ending in a victory. In normal events, a 4-0 win over Arbroath would be a footnote in Rangers' season rather than a unique occasion.

By their nature, knockout matches are unreliable reference points. Yet a series of failures suggests that there is more than misfortune to contend with. McCoist could point to the unexpected gaffe by Neil Alexander that allowed Falkirk to score the late, decisive goal in their 3-2 Scottish Communities League Cup win last September. That came after Rangers were forced to rally in the second-half, though, having fallen two goals behind. Their frantic chasing of the game was the consequence of a generally lacklustre display.

They also ended the match with Allan McGregor being the only member of McCoist's strongest line-up not involved. It is legitimate to point out that of the four strikers used in Sunday's William Hill Scottish Cup defeat by Dundee United – David Healy, Sone Aluko, Salim Kerkar and Andy Little – only Aluko has the form or the recent pedigree of a proven Clydesdale Bank Premier League performer.

Healy's glories lie in the past, Kerkar has been a marginal figure, and Little is a young player whose development has been hampered by injuries and who Walter Smith was convinced would only flourish at right-back.

McCoist is surrounded by mitigating factors, and there is no mistaking the extent of the club's predicament. Administration is no longer a vague prospect and the Rangers manager talks about the future with a grave tone. The sale of Nikica Jelavic on the last day of the January transfer window without a replacement being signed was an admission that, whatever financial troubles exist at Ibrox, they are more important to Craig Whyte than the team's title challenge.

Other issues remain, though. Rangers were knocked out of the Champions League qualifiers by Malmo, then failed to overcome NK Maribor in the preliminary stages of the Europa League. Neither side could be considered among even the middle tier of continental teams. Malmo fell at the next stage to Dinamo Zagreb, then moved into the Europa League and lost all but one of their group games, a 0-0 draw with AZ Alkmaar. Maribor suffered the same fate in their six group games, losing five and drawing one.

Some failings have been recurring. Rangers have often struggled to play at a high tempo this season, even before Steven Naismith injured his knee, and the sole tactic to break opponents down has been to hit long balls into the channels for Jelavic. Despite hoarding a number of small, wide players in his squad – Gregg Wylde, Aluko, Naismith, Alejandro Bedoya, Juanma Ortiz and even Matt McKay, who played centrally for Brisbane Roar but has been designated as a player for the left flank at Ibrox – Rangers have tended to be unable to count upon their wingers.

The over-reliance on Jelavic was evident even before he was sold, with the Croat having scored 14 SPL goals, five more than Naismith, the second-top scorer at the club despite having last played in October. Even during the run of results that left Rangers, briefly, 15 points ahead of Celtic, the team often performed flatly but still found the means to gain points. That custom has been misplaced since back-to-back defeats to St Mirren and Celtic last December.

Statistics offer some solace to McCoist since Rangers have scored only one goal fewer than Celtic in the league and conceded two goals fewer. Yet the Ibrox side have lost three times on their travels in the league this season, and have slumped since establishing that lead over the rivals.

There have been moments of inspiration by McCoist, and his team was trailing to Celtic at half-time at Ibrox last September following a rare mistake by McGregor. The manager's words during the interval, reminding the players that they owed a debt to their goalkeeper's past heroics, were rousing and Rangers then swept Celtic aside. Other matches have petered out, though, and the balance in midfield between Maurice Edu and Steven Davis has never wholly convinced.

The latter has flitted in and out of form, and it seems a compromise that McCoist continues to select Lee Wallace and Sasa Papac on the left. The Bosnian is a centre-back converted to a full-back, but has played in midfield, while Wallace is a defender also occasionally pressed into service further up the pitch. Kyle Bartley, too, is being played out of position at right-back.

McCoist deserves time, and a less fraught working environment, before judgment is passed. Managers suffer periods of adversity but the successful ones learn the habit of surviving them. .

Even without a top-class striker, Rangers should be good enough to overcome most of their domestic opponents. McCoist can cite the difficulties around the club, but organisation, tactics, the spirit of his players and even their form are still directly under his control. He is facing a stark test.