It's a GC issue
2013-07-27T01:35:29.993-0400: 3132.291: [Full GC 3132.291: [CMS: 24117248K->24117247K(24117248K), 17.6407850 secs] 26004735K->26004729K(26004736K), [CMS Perm : 38463K->38463K(64412K)], 17.6409100 secs] [Times: user=17.63 sys=0.00, real=17.64 secs]
Heap after GC invocations=94 (full 163):
...
concurrent mark-sweep generation total
24117248K, used 24117247K [0x000000023ae00000, 0x00000007fae00000, 0x00000007fae00000)
2013-07-27T01:35:47.635-0400: 3149.933: [Full GC 3149.933: [CMS
Full GC blocks all the threads, leading to the connection timeouts
You an see, that after the GC cycle, there is no free space in the tenured generation
You may try to increase the heap and/or change yound/old gen ratio, decrease the number of facets
Volodymyr