From my experience with Amex the amount you can spend varies depending on a number or factors:
-The highest amount you repaid (on-time) in the last 24 months
-Your payment history in the last 24 months (paid within due date/30days)
-Your overall account risk rating (current exposure across all Amex products, credit score, membership tenure etc).
-The types of businesses you are spending at (eg a supermarket would be considered a safer/less risky transaction than a massage parlour
)
It is a very complicated system and is constantly changing, basically the authorising system performs a cost benefit analysis of Amex approving vs declining a particular transaction.
If you are spending 'out of pattern' generally it's best to call them first so they can run a dummy transaction to see if it will go through. They can then put a support on your account to prevent the charge from being referred in or declined.
Alternatively I have seen in the past instances where customers arranged to have a bank guarantee/financial evidence added to their account that would ensure that spending to a certain level would be guaranteed.
Alternatively you might prefer an Amex credit card if you prefer to keep things simpler but I think you will find once you have shown you can repay on time that the amount you can spend will be greatly increased in the future.