Valley were held to a frustrating goalless draw against Lye Town at Butlin Road.
The two relegation-threatened sides shared the points after a predictably scrappy affair which featured a penalty save on the half hour mark from Town keeper Paul Hathaway.
A week on from an encouraging display against Hinckley, Town boss Ian King was forced into two changes to his line-up from that much needed-win home win - with Dan Summerfield ill and Caine Elliott deemed not fit enough to start.
Robbie Paratore and new signing Kartell Dawkins replaced them in King's midfield, as Rugby looked to register back-to-back league victories for the first time this season.
The hosts nearly broke the deadlock early doors from a pre-rehearsed corner routine, with skipper Josh Thomas having a shot blocked and Tyreace Brown lifting the loose ball over the bar.
Bodi Thistleton sent in a threatening high cross on the overlap, but the ball drifted just out of play, with the young Burton Albion defender then narrowly failing to connect when a corner reached him on the left-hand side.
Chris Clements dragged one wide, as Rugby's decent enough start continued, although at the other end Joe Palmer and Reinaldo Forbes did both cause some worry with crosses from their respective wings.
It was, however, against the run of the play when Lye were awarded their penalty after Brown brought down Nathanial Dixon in the box, with Hathaway down well to his right to keep out Palmer's effort from the spot.
The visitors then enjoyed their best spell of the game, with Forbes's relatively-weak header easily gathered by Hathaway and Palmer's strong strike from the edge of the area blocked by Will Ronald.
A further low shot from Palmer hit the post after Jahvan Davidson-Miller had given the ball away, before Valley ended the half well with a series of half-chances of their own.
Trey Charles's effort at the back post was blocked away for a corner and an unconventional attempt at a volley by Davidson-Miller was caught by Lye keeper Ben Newey.
Daniele Reka did cannon one back off the crossbar with an impressive acrobatic strike, but he was ruled to be in an offside position when doing so, with Thomas ending the half with a good tackle to deny Dixon a shooting opportunity.
Rugby again went close to the game's opening goal in the early minutes of the new period, with Newey at full stretch to palm away Davidson-Miller's curling effort from the edge of the penalty box.
Charles's low cross was cleared away from the goalmouth, before Davidson-Miller guided a great opportunity wide of the frame after he had ran on to Darnell's instinctive ball over the top of the away defence.
Reka's effort on the turn lacked power after he had done well to retain possession in the first place, with Brown heading away a dangerous cross from Palmer in a rare attacking highlight from the visitors.
Brown's downward header to Chris Clements's corner was scrambled around his post by Newey, with Thomas also heading one wide after Clements had picked him out with a cross from the left.
Paratore failed to bring down a Clements pass after neat interchange play from the home side, with Charles then twice denied by defensive blocks.
Lye sub Matt Saunders's low shot from a tight angle was also deflected off-target, before Lye were reduced to ten men in added-time when their defender Michael Adanusi was dismissed for his second yellow card of the game - both awarded for pulling back the lively Reka.
There was therefore little time for Rugby to take advantage of the numerical supremacy, although Newey did easily catch a Josh Thomas header in the dying moments.
