File conversion from MP4 stops early, outputting partial file

I have a ton of MP4 videos that need to be re-encoded from MPEG-4 to AVC/H.264. I've run into a pretty serious problem and I've barely started.

I've noticed that some of the files aren't converted completely. ffmpeg stops early and I'm left with a partial video.

Here's the output from one of them:

...
...
frame=21724 fps=1207 q=17.8 size= 29486kB time=00:12:04.48 bitrate= 333.4kbits/s
frame=22377 fps=1209 q=13.9 size= 30372kB time=00:12:26.48 bitrate= 333.3kbits/s
frame=23027 fps=1212 q=10.5 size= 31254kB time=00:12:47.97 bitrate= 333.4kbits/s
Truncating packet of size 320 to 192
[aac @ 02c06000] decode_band_types: Input buffer exhausted before END element found
Error while decoding stream #0:1
[mov,mp4,m4a,3gp,3g2,mj2 @ 003dbba0] stream 1, offset 0x3171489: partial file
AV Filter told us it has a frame available but failed to output one
frame=23557 fps=1214 q=16.7 Lsize= 31984kB time=00:13:05.54 bitrate= 333.5kbits/s

video:19376kB audio:12274kB global headers:0kB muxing overhead 1.054033%

I've done searches but can't find anything that addresses this issue. On one hand, it's probably not specifically an ffmpeg problem because attempts to convert with other software resulted in the same length partial file. On the other hand, ffmpeg still feels like the best tool for getting around it. I just don't know how.