Does he "grow tired" or does the grinta and firing up simply stop to work at one point when you do it week in week out?
I doubt he is still firing them up week in week out with motivational speeches. It seems he himself loses motivation once he doesnt get the transfers that he wants and that spills over into the team themselves.
Like he starts out his tenure super charged and motivated. The club has faith in him and the future has a lot of promise. He starts with a mediocre squad that he gets to over-perform and punch above their weight and so confidence (including his own) become sky high and he sets the expectation in his team's minds that they can win a trophy or two and they rise up to that and achieve it.
Then summer comes and he tells the club I can take the team to the next level but I need some expensive transfers. I made this team punch above their weight but if you want more, then sign me XYZ players. The club says no we cant afford that. You have to do with what you have got + 1 or 2 okay signings. He doesnt feel this is enough and they have a fall out and he goes into the new season believing deep down that his squad is not good enough.
Then when a few results go against his team, he starts voicing his complaints to the media that he asked for more and didnt get what he asked for and that the club should have listened. The deep down belief becomes public and naturally spills over into the team. the squad starts believing that they are not good enough because they know he thinks that, and so his motivational speeches either become ineffective or maybe he even stops doing them. He lowers the expectations that they have to rise up to and so they deliver that lower expectation and they stop going above and beyond.
Then comes a coach like Allegri that tells them that while they might not be as powerful as the best teams, they can put up a serious challenge and achieve lots of great things. He sets the expectation high again and so players rise up to that level and go above and beyond. They are not good enough to be the best but they realize that if they go above and beyond and with some little luck they can get really close to the powerful clubs.
Its all about belief. If your team genuinely believe that they can reach a high level. If you have buy-in as their manager in the goals that you set and these goals arent insane then they will rise up to it. If you set very high expectations/goals but they dont buy into it and think you are delusional they will crash miserably because the goal will just be a massive source of stress and anxiety instead of a motivator.
If you set low expectations on even a top player, if that player isnt an egotistical maniac like Ronaldo with so much self-belief, your top player will deliver at this low level expectation. Arsenal is a club whose players are victim of low expectations. Wenger doesnt instill belief in them that they can achieve great things even though they have a good squad. When they are close to the top, they never believe that they are good enough to be champions so they choke and default to 4th. The expectation from the fanbase is a source of stress and anxiety to them so they always fuck it up. They (including Wenger) dont believe that they are genuine champions.
at the same time they know that the club doesnt expect anything more than top 4 so they deliver to that level. This season I am not even sure they believe they are good enough for top 4.
Anyway, when Conte stops believing that his squad can achieve greater things (due to not getting the transfers he wants), he lowers expectations for his team and so they perform to that lower level. So when this happens, either sack him and get in someone with more belief, or back him up and get him the players he wants. My boss cant motivate me to do great things if I over heard him saying that I am really not good enough.