I have this problem, too - NetFlix worked beautifully before I updated to ICS / HTC Sense 3.6, but after the upgrade there is a lot of quirky behavior all around the phone.
You may notice that, once NetFlix starts dimming, other video apps (YouTube, for example) start doing it, too. I had an app called MX Player that allows for brightness adjustment while watching a video, and I found that if I started a video with that app, then dimmed and re-upped the brightness while watching a video, other apps would then have their brightness fixed - but the phone started to lock up doing this. Figuring this was the root problem - if it can FIX it, perhaps it is CAUSING it - I removed MX Player; the behavior persists.
Alternatively, if NetFlix offers captions for a video, I found that by hitting the caption button BEFORE the screen auto-dims, then touching the screen outside the caption window, it will hide the caption window behind the video and play menu. You can then press play and watch your video at proper brightness - but the play menu stays visible, and this can lead to locking up NetFlix and potentially pulling the battery to reboot. If you do this, you can't let the screen orientation change while watching the video, and you can't tap the video to hide the menu - either will immediately dim the screen again.
I hope the workarounds help, but I wish I could determine if this is an ICS, Sense 3.6, or NetFlix problem, so I could complain to the right company without fear they'll blame one of the other two.
Edit: from the response given, sounds like an upgrade issue. Will try a factory reset and post back
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