The most obvious downside is that it creates perverse incentives -- potential customers benefit if you fail. It also telegraphs a lack of...I don't know what the word is. Tenacity? It's kind of like putting a bounty on your own head so that at least somebody can benefit if you die. You really want people to be invested in your survival.
It also limits what you can do with your program. If your program uses code you don't have a license to release, you can't open-source it.
It's debatable customers benefit if a company fails and open sources their product. The customer, assuming they're willing and able to install it, misses out on any further upgrades (rare is the salvaged open source that goes anywhere) and support. Though I don't discount that there is _some_ benefit and that many customers might over-estimate that benefit.
It also limits what you can do with your program. If your program uses code you don't have a license to release, you can't open-source it.