No, Discord server boosts are not a permanent fix to a problem. When purchased, they are only intended to be used as a temporary solution to buff a server.
When you purchase a server boosting subscription, this will improve the server until the server boost is cancelled. Being a subscription, the payment for the boost is taken each month.
If you were to keep the server booster then technically it would be a permanent solution to the problem. However, it is not a one time purchase and can quickly become expensive.
There is currently no option to purchase a permanent server boost, which many users would benefit from. When a person is a Nitro member, they are able to boost one server for seven days, which is useful.