The Gunners face league leaders Leicester City on Sunday, with the result of that game likely to be a determining factor in who ends up as title winners come the end of the campaign.
Arsene Wenger’s side have fallen away in recent weeks and are now five points off top after once having been out in front.
That has led to many questioning if they have the mentality to be champions once again, and Smith says the loss to Chelsea at the end of January also raised those questions.
“They have a really poor record in terms of staying at the top at the end of seasons,” he told Sky Sports.
“Part of that is the squad has not been strong enough, and it's partly down to mental weakness too. There has been a psychological barrier and we've seen that twice against Chelsea this season.”
“Are they mentally strong enough now to push on, to beat Leicester on Sunday, and to push on again during the difficult away games to come? Are they strong enough to get their talent across? That's still the big question for me."
This weekend’s clash is certainly looking to be a big one for Arsenal, with it looking likely to have a huge impact on how the rest of their season fares.
They will be confident of securing all three points though, having beat Claudio Ranieri’s side earlier in the campaign and will hope they can use that blueprint for further success.
If they can win, it is sure to be a huge boost to their title hopes, especially given how easily rivals Manchester City were dispatched last time around.