The custom oplog follower we're using creates a tailable cursor as follows:

mongo.getDB("foo").getCollection("bar").find(criteria).limit(0).skip(0)
.hint(new BasicDBObject("$natural", 1))
.addOption(Bytes.QUERYOPTION_TAILABLE)
.addOption(Bytes.QUERYOPTION_AWAITDATA)
.addOption(Bytes.QUERYOPTION_NOTIMEOUT);

After a couple million writes to the database, the cursor throws an exception like this:

com.mongodb.MongoException$CursorNotFound: cursor 0 not found on server localhost/127.0.0.1:10120
at com.mongodb.DBApiLayer$Result.init(DBApiLayer.java:394)
at com.mongodb.DBApiLayer$Result._advance(DBApiLayer.java:454)
at com.mongodb.DBApiLayer$Result.hasNext(DBApiLayer.java:421)
at com.mongodb.DBCursor._hasNext(DBCursor.java:464)
at com.mongodb.DBCursor.hasNext(DBCursor.java:484)

The process waits a second and then attempts to create a new cursor, using the same method. This succeeds, but the same exception is thrown 5-10 seconds later. Once the initial exception is thrown, subsequent exceptions occur very frequently (the initial exception may take a long time to occur after the process starts). This exception occurs so frequently, that our process falls far behind in processing oplog entries.