I'm having what I take to be the same issue, frequent disconnects followed by the miner being unable to connect: 

INFO 19:25:47: GPU0 Accepted share 174ms [A:253, R:1]                                               
INFO: Detected new work: 361                           
Temp: GPU0: 63C                                        
GPU0: 70 Sol/s                                                          
Total speed: 70 Sol/s                                       
INFO 19:26:11: GPU0 Accepted share 178ms [A:254, R:1]                                                                                                                                                              
ERROR: Lost connection with the server.             
INFO: Attempt to restore connection.                
ERROR: Stratum subscribe timeout

(retry attempts repeated ad nauseum) 

If I try to reconnect:

+-------------------------------------------------+
|         EWBF's Zcash CUDA miner. 0.3.4b         |
+-------------------------------------------------+
INFO: Current pool: zec.poolmining.org:3036
INFO: Selected pools: 1
INFO: Solver: Auto.
INFO: Devices: All.
INFO: Temperature limit: 90
INFO: Api: Disabled
---------------------------------------------------
ERROR: Stratum subscribe timeout

Have not had any issues pointing the same miner at other pools.

nslookup / traceroute on zec.poolmining.org get reasonable results.