Beale’s side have won their last three matches in all competitions with three clean sheets, but they put in a poor display to just edge out Motherwell at the weekend.
The Rangers manager’s stock amongst the fans is at an all-time low and many are keen to see the board sack him despite recent results.
Miller admitted that Beale is now working on a game-to-game basis and any defeat could spell the end of his time at Rangers.
However, he believes there is hope as he is certain that Rangers will reach the Europa League knockout stages and win the Scottish League Cup in the coming months.
The former Rangers man conceded that Beale needs to keep winning but feels if he can make it until the end of December, the mood around the club could change.
Miller said on Clyde 1’s Superscoreboard: “If Rangers fail on Wednesday or even fail to win on Saturday then there is going to be serious discussions at Ibrox.
“But I fast forward to December and you don’t play Celtic until the end of December.
“I think Rangers will be in the knockout stages of the Europa League in the first week of December.
“The second week of December, I believe Rangers will go on and lift the League Cup and it needs to get that point.
“I am not saying it with any great confidence based on what I watched yesterday [Sunday] but the reality is that they are not playing well but they still managed to beat potentially the third-best team in the country at this moment in time in Motherwell.
“If he can get to that point there is going to be some level of positivity and to get there, he needs to keep winning.”
Many believe Beale cannot lose another game in domestic football until the next Old Firm clash against Celtic at the end of December.