I am looking for a verb meaning "to make something more robust", especially in a software engineering context.
Is "to robust" correct and understandable? "Robustify" seems to be another candidate but does not seem so common.
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There's no single word to describe making software more robust. Some ways of making software more robust are: simplify, debug, re-factor (especially functional decomposition and code re-use), make the interface more user friendly, make the program resilient to input errors and even recover from some runtime errors, etc.
"Harden" comes to mind, as in hardening a computer system. See https://en.wikipedia.org/wiki/Hardening_(computing)