I'm still seeing problems with iOS 7.0.4, unfortunately. Is the below consistent with what you're seeing or is this perhaps another type of issue?
My test server is running Moodle on Apache and one user can consistently replicate this with two iPads on iOS 7.0.4. The HTTP 407s in the logs below is a Moodle thing. As you can see the cookie is not sent with the range requests:
access_log:
xxx.yyy.zzz.227 - - [22/Nov/2013:23:11:18 +0000] "GET /pluginfile.php/21/mod_videofile/videos/0/trailer_test.mp4 HTTP/1.1" 200 3711807 "http://xyz.bitnamiapp.com/mod/videofile/view.php?id=2" "Mozilla/5.0 (iPad; CPU OS 7_0_4 like Mac OS X) AppleWebKit/537.51.1 (KHTML, like Gecko) Version/7.0 Mobile/11B554a Safari/9537.53"
xxx.yyy.zzz.227 - - [22/Nov/2013:23:11:19 +0000] "GET /pluginfile.php/21/mod_videofile/videos/0/trailer_test.mp4 HTTP/1.1" 407 12818 "-" "AppleCoreMedia/1.0.0.11B554a (iPad; U; CPU OS 7_0_4 like Mac OS X; en_us)"
...
forensic_log:
+Uo-kj38AAAEAAH0O5MEAAAAJ|GET /pluginfile.php/21/mod_videofile/videos/0/trailer_test.mp4 HTTP/1.1|Host:xyz.bitnamiapp.com|Referer:http%3a//xyz.bitnamiapp.com/mod/videofile/view.php?id=2|Accept-Encoding:gzip, deflate|Accept:text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8|Accept-Language:en-us|Cookie:MoodleSession=24gkspshgl8027k3l7p2cor631|Connection:keep-alive|DNT:1|User-Agent:Mozilla/5.0 (iPad; CPU OS 7_0_4 like Mac OS X) AppleWebKit/537.51.1 (KHTML, like Gecko) Version/7.0 Mobile/11B554a Safari/9537.53
+Uo-kkH8AAAEAAB2cL4IAAAAA|GET /pluginfile.php/21/mod_videofile/videos/0/trailer_test.mp4 HTTP/1.1|Host:xyz.bitnamiapp.com|Range:bytes=0-1|X-Playback-Session-Id:DF1039A4-571B-4EB8-BFFB-EF07CD730CA2|Accept-Encoding:identity|Accept:*/*|Accept-Language:en-us|Connection:keep-alive|User-Agent:AppleCoreMedia/1.0.0.11B554a (iPad; U; CPU OS 7_0_4 like Mac OS X; en_us)
-Uo-kj38AAAEAAH0O5MEAAAAJ
-Uo-kkH8AAAEAAB2cL4IAAAAA
...