Tenant always short on rent, MGMT company not collecting late fee

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So I have this property in a D neighborhood (Ybor city, Tampa) and I have a management company managing it. The tenant paid the first and second months promptly, the third was late and the forth which was supposed to be paid on 06/10/2019 was paid partially until now (missing $70). After the first month this has happened I asked the management company to start charging late fees which they said they do but they don't enforce them because they aren't being transferred to the owner balance. So I asked the management company to split the fees with me which is pretty uncommon from asking around. Now late fees are stacking up on my balance as well as the missing rent.

This month the tenant hasn't fully paid his rent nor did he pay his late fees and tomorrow he's supposed to complete another payment which I don't see him fully doing so. I feel like my management company is sloppy / too forgiving with this property. Should I go ahead and start an eviction or should I just let the income continue until I finish the lease and then not renew it ?