Should companies invest in innovation in today's down market? It depends on what type of innovation. In this Forbes article, the authors note that DuPont continued to invest in R&D in the 1930s and discovered neoprene (synthetic rubber), an enormously successful product.
But this analysis lacks real data on investing in technology as opposed to innovation. How many companies lost how much in R&D and was it worth it?
Innovation is creating and validating a solution concept that meets customer needs. It is not investing in R&D. In any market, investing lots of capital in R&D can be (an usually is) extremely risky.
A better way to invest in innovation is to figure out what the unmet customer needs are and then develop solutions based on known and proven technology first. If this isn't possible, then investing in R&D when the needs are known has much lower risk.
So the right question isn't, "should companies invest in innovation?" The right question is "what is innovation?"