When one of masters is unreachable all other replica sets work too slow in mongodb 2.6.11 and web application throws error 71
Replica sets are individual entities unless you are sharing resources among them like CPU,RAM,Disk... running multiple mongods in a single server. 

I believe your case is that on a sharded cluster scatter-gather queries speed is determined by the slowest shard, so when one shard gets slow all scatter-gather queries will turn slow.