You're likely hitting max_concurrency. Colin Mollenhour has made significant updates to the Redis integrations (and his Redis Session integration) in his Github repo modules.

I suggest you upgrade to the most recent version, which batches SUNIONs to avoid massive wait times.

Aside from this I've seen max_concurrency hit while bots are crawling. Because of this we've, on occasion, made updates to the Bot settings in Collin's module. 

See here for more information:

https://github.com/colinmollenhour/Cm_RedisSession#bot-detection