Most replies to this are making a category error. Parser combinators aren't a parsing technology, they're a library interface. You can use any parsing technology as a backend to an interface that is built in terms of combinators. That most of them are essentially recursive-descent is a result of common implementation decisions, not a requirement of the interface.
And that's why parsing research doesn't pay much attention to it - it's an interface, not a different approach to handling data while parsing. It's all about ergonomics of using a parser, not about the capability and performance characteristics of parsing.
Should more research pay attention to that? Probably. BISON/YACC/ANTLR are all hell to use. Combinator-based libraries are easier, but current designs lack things like extending parsers without modifying them. There's a lot of research that could be done that would care about this aspect of parsers, but it doesn't seem to be for now.
And that's why parsing research doesn't pay much attention to it - it's an interface, not a different approach to handling data while parsing. It's all about ergonomics of using a parser, not about the capability and performance characteristics of parsing.
Should more research pay attention to that? Probably. BISON/YACC/ANTLR are all hell to use. Combinator-based libraries are easier, but current designs lack things like extending parsers without modifying them. There's a lot of research that could be done that would care about this aspect of parsers, but it doesn't seem to be for now.