The visitors are without a permanent manager or chairman and top striker Chris Zebroski failed to appear for the 1-0 FA Cup defeat to lower league Hampton and Richmond Borough.
Previous chairman Mark Jewell stood down earlier this month and manager Andy Hessenthaler left to join Dover and Eastleigh have lost their two matches under caretaker-chief Ben Strevens.
Halifax recorded their first win in 11 games with their 2-0 FA Cup victory over Warrington on Tuesday and have their sights set on a first league win since beating Gateshead 1-0 on August 27.
Halifax chief Jamie Fullarton had just four players on the bench on Tuesday due to a lengthy injury list but he said: “It’s pleasing that the players who had the opportunity showed they are capable of performing, contributing and being part of it.
“I’ll harp back to the first couple of weeks where I said it was about the group, and one person’s misfortune is someone else’s opportunity. They must take the opportunity and, if they do, they stay in.”