Repeated promises without payment are a different problem from a slow-paying client. The pattern ("payment is coming this week," then silence, then another promise) usually means the client is managing cash flow at your expense, whether intentionally or not.
Move from email to a phone call. A direct conversation is harder to defer than a written message and often surfaces the real obstacle: a disputed line item, an internal approval bottleneck, or a genuine cash problem they haven't said outright. Ask directly: "Is there anything on the invoice you'd like to discuss before we settle this?" That question either resolves a hidden objection or makes clear there isn't one.
After a call with no resolution, shift to written-only communication with explicit deadlines and consequences stated in every message. "If payment is not received by [Date], I will apply the late fee outlined in our contract and suspend further work." Keep the tone factual. The goal at this stage is a paper trail, not a conversation.