MCP23017 Failing After Several Minutes?
How is the hardware configured? Do you know how much current the LEDs are drawing? The datasheet says each pin can source or sink 25mA. That is reasonable for a typical, indicator LED, but you could be pushing it. Plus, the max current into Vdd is 125mA. It could be possible that the chip is shutting down the outputs until a hard reset to prevent overheating. If you are using transistors for the LEDs, it wouldn't matter. However, I'd be interested to see if you only used a couple LEDs and increased the series resistance for each such that they drew less current if that would fix the issue or not.

Edit

Pull the RESET pin up to 5V with a 10kΩ resistor. If not, it will just be floating. Once it drops below a certain threshold, it will reset the port expander.