This is similar to CSHARP-754, but with a different call stack.
Like in that bug, the only way we have found to fix the issue is to recycle the application pool of the web service hitting Mongo.

Connection string like the following:
mongodb://host1:27017,host2:27017,arbiterOnWindows:27017/?replicaSet=my_replica_set;socketTimeout=120000ms;maxPoolSize=200

The following 2 stack traces alternate:

Stack trace 1:
2013-09-18 13:14:39,945 ERROR - Unable to connect to a member of the replica set matching the read preference Primary: The requested name is valid, but no data of the requested type was found.
MongoDB.Driver.MongoConnectionException: Unable to connect to a member of the replica set matching the read preference Primary: The requested name is valid, but no data of the requested type was found. ---> System.Net.Sockets.SocketException: The requested name is valid, but no data of the requested type was found
at System.Net.Dns.GetAddrInfo(String name)
at System.Net.Dns.InternalGetHostByName(String hostName, Boolean includeIPv6)
at System.Net.Dns.GetHostAddresses(String hostNameOrAddress)
at MongoDB.Driver.MongoServerAddress.ToIPEndPoint(AddressFamily addressFamily)
at MongoDB.Driver.MongoServerInstance.GetIPEndPoint()
at MongoDB.Driver.Internal.MongoConnection.Open()
at MongoDB.Driver.Internal.MongoConnection.SendMessage(BsonBuffer buffer, MongoRequestMessage message, WriteConcern writeConcern, String databaseName)
at MongoDB.Driver.Internal.MongoConnection.SendMessage(MongoRequestMessage message, WriteConcern writeConcern, String databaseName)
at MongoDB.Driver.Internal.MongoConnection.RunCommandAs[TCommandResult](String databaseName, QueryFlags queryFlags, CommandDocument command, IBsonSerializer commandResultSerializer, IBsonSerializationOptions commandResultSerializationOptions, Boolean throwOnError)
at MongoDB.Driver.Internal.MongoConnection.RunCommandAs[TCommandResult](String databaseName, QueryFlags queryFlags, CommandDocument command, Boolean throwOnError)
at MongoDB.Driver.MongoServerInstance.Ping(MongoConnection connection)
at MongoDB.Driver.MongoServerInstance.Connect()
at MongoDB.Driver.Internal.MultipleInstanceMongoServerProxy.<>c_DisplayClassd.<ConnectInstance>b_c(Object _)
— End of inner exception stack trace —
at MongoDB.Driver.Internal.MultipleInstanceMongoServerProxy.ThrowConnectionException(ReadPreference readPreference)
at MongoDB.Driver.Internal.MultipleInstanceMongoServerProxy.Connect(TimeSpan timeout, ReadPreference readPreference)
at MongoDB.Driver.Internal.MultipleInstanceMongoServerProxy.ChooseServerInstance(ReadPreference readPreference)
at MongoDB.Driver.MongoServer.AcquireConnection(ReadPreference readPreference)
at MongoDB.Driver.MongoCursorEnumerator`1.AcquireConnection()
at MongoDB.Driver.MongoCursorEnumerator`1.GetFirst()
at MongoDB.Driver.MongoCursorEnumerator`1.MoveNext()
at System.Linq.Enumerable.WhereSelectEnumerableIterator`2.MoveNext()
at System.Collections.Generic.List`1..ctor(IEnumerable`1 collection)
at System.Linq.Enumerable.ToList[TSource](IEnumerable`1 source)

Stack trace 2:
2013-09-18 13:13:44,735 ERROR - Unable to connect to a member of the replica set matching the read preference Primary
MongoDB.Driver.MongoConnectionException: Unable to connect to a member of the replica set matching the read preference Primary
at MongoDB.Driver.Internal.MultipleInstanceMongoServerProxy.ThrowConnectionException(ReadPreference readPreference)
at MongoDB.Driver.Internal.MultipleInstanceMongoServerProxy.Connect(TimeSpan timeout, ReadPreference readPreference)
at MongoDB.Driver.Internal.MultipleInstanceMongoServerProxy.ChooseServerInstance(ReadPreference readPreference)
at MongoDB.Driver.MongoServer.AcquireConnection(ReadPreference readPreference)
at MongoDB.Driver.MongoCursorEnumerator`1.AcquireConnection()
at MongoDB.Driver.MongoCursorEnumerator`1.GetFirst()
at MongoDB.Driver.MongoCursorEnumerator`1.MoveNext()
at System.Linq.Enumerable.WhereSelectEnumerableIterator`2.MoveNext()
at System.Collections.Generic.List`1..ctor(IEnumerable`1 collection)
at System.Linq.Enumerable.ToList[TSource](IEnumerable`1 source)