So I was able to resume by doing this:
First I make my app remember the "totalBytesRead" and "totalBytesExpectedToRead".
[operation setDownloadProgressBlock:^(NSUInteger bytesRead, long long totalBytesRead, long long totalBytesExpectedToRead) {...}
Then, when the download fails, I have a retry button. When the user clicks the button, I call this code
NSMutableURLRequest *request = [NSMutableURLRequest requestWithURL:@"www.myfileURL.com/file.mp4" cachePolicy:NSURLRequestUseProtocolCachePolicy timeoutInterval:10];
NSString* range = [NSString stringWithFormat:@"bytes=%lli-%lli", totalBytesRead, totalBytesExpectedToRead];
[request setValue:range forHTTPHeaderField:@"Range"];
operation = [[AFHTTPRequestOperation alloc] initWithRequest:request];
operation.outputStream = [NSOutputStream outputStreamToFileAtPath:myPath append:YES];
Make sure you properly set the http header for range in the format "bytes=fromBytes-totalBytes". An example would be "bytes=3200-12000"
Make sure that when you make the new operation, you change the output stream to APPEND:YES. This is so your downloaded bytes append to the previously downloaded ones.