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ffmpeg video encoding never begins with -ss and -t flags
I'm trying to cut a video in two parts using two commands:
ffmpeg -i "a.mkv" -c:v libx264 -preset slow -crf 8 -c:a libfdk_aac -vbr 5 -ss 00:03:30 -t 00:01:30 "h.264/a1.mp4"
ffmpeg -i "a.mkv" -c:v libx264 -preset slow -crf 8 -c:a libfdk_aac -vbr 5 -ss 00:10:30 -t 00:01:30 "h.264/a2.mp4"

When I run either one of these, ffmpeg starts but does not begin encoding. The output is constantly fps=0. Here is the output:
ffmpeg version N-73755-g1c5b712 Copyright (c) 2000-2015 the FFmpeg developers
  built with gcc 4.8 (Ubuntu 4.8.2-19ubuntu1)
  configuration: --prefix=/root/ffmpeg_build --pkg-config-flags=--static --extra-cflags=-I/root/ffmpeg_build/include --extra-ldflags=-L/root/ffmpeg_build/lib --bindir=/root/bin --enable-gpl --enable-libass --enable-libfdk-aac --enable-libfreetype --enable-libmp3lame --enable-libopus --enable-libtheora --enable-libvorbis --enable-libvpx --enable-libx264 --enable-libx265 --enable-nonfree
  libavutil      54. 28.100 / 54. 28.100
  libavcodec     56. 49.101 / 56. 49.101
  libavformat    56. 40.101 / 56. 40.101
  libavdevice    56.  4.100 / 56.  4.100
  libavfilter     5. 23.100 /  5. 23.100
  libswscale      3.  1.101 /  3.  1.101
  libswresample   1.  2.101 /  1.  2.101
  libpostproc    53.  3.100 / 53.  3.100
Guessed Channel Layout for  Input Stream #0.1 : stereo
Input #0, matroska,webm, from 'a.mkv':
  Metadata:
    ISRC            : Video:x264vfw - H.264/MPEG-4 AVC codec Audio0:Speakers (Realtek High Definition Audio) Audio1:Microphone (Realtek High Definition Audio)
    ENCODER         : Lavf56.40.101
  Duration: 00:16:01.34, start: 0.000000, bitrate: 236851 kb/s
    Stream #0:0: Video: h264 (High 4:4:4 Predictive), yuv420p, 1920x1080 [SAR 1:1 DAR 16:9], 60 fps, 60 tbr, 1k tbn, 120 tbc (default)
    Metadata:
      ENCODER         : Lavc56.49.101 libx264
    Stream #0:1: Audio: pcm_s16le, 48000 Hz, 2 channels, s16, 1536 kb/s (default)
[libx264 @ 0x36ce0e0] using SAR=1/1
[libx264 @ 0x36ce0e0] using cpu capabilities: MMX2 SSE2Fast SSSE3 SSE4.2 AVX LZCNT
[libx264 @ 0x36ce0e0] profile High, level 5.0
[libx264 @ 0x36ce0e0] 264 - core 142 r2389 956c8d8 - H.264/MPEG-4 AVC codec - Copyleft 2003-2014 - http://www.videolan.org/x264.html - options: cabac=1 ref=5 deblock=1:0:0 analyse=0x3:0x113 me=umh subme=8 psy=1 psy_rd=1.00:0.00 mixed_ref=1 me_range=16 chroma_me=1 trellis=1 8x8dct=1 cqm=0 deadzone=21,11 fast_pskip=1 chroma_qp_offset=-2 threads=6 lookahead_threads=1 sliced_threads=0 nr=0 decimate=1 interlaced=0 bluray_compat=0 constrained_intra=0 bframes=3 b_pyramid=2 b_adapt=2 b_bias=0 direct=3 weightb=1 open_gop=0 weightp=2 keyint=250 keyint_min=25 scenecut=40 intra_refresh=0 rc_lookahead=50 rc=crf mbtree=1 crf=8.0 qcomp=0.60 qpmin=0 qpmax=69 qpstep=4 ip_ratio=1.40 aq=1:1.00
[libfdk_aac @ 0x36a6f00] Note, the VBR setting is unsupported and only works with some parameter combinations
Output #0, mp4, to 'h.264/a1.mp4':
  Metadata:
    ISRC            : Video:x264vfw - H.264/MPEG-4 AVC codec Audio0:Speakers (Realtek High Definition Audio) Audio1:Microphone (Realtek High Definition Audio)
    encoder         : Lavf56.40.101
    Stream #0:0: Video: h264 (libx264) ([33][0][0][0] / 0x0021), yuv420p, 1920x1080 [SAR 1:1 DAR 16:9], q=-1--1, 60 fps, 15360 tbn, 60 tbc (default)
    Metadata:
      encoder         : Lavc56.49.101 libx264
    Stream #0:1: Audio: aac (libfdk_aac) ([64][0][0][0] / 0x0040), 48000 Hz, stereo, s16 (default)
    Metadata:
      encoder         : Lavc56.49.101 libfdk_aac
Stream mapping:
  Stream #0:0 -> #0:0 (h264 (native) -> h264 (libx264))
  Stream #0:1 -> #0:1 (pcm_s16le (native) -> aac (libfdk_aac))
Press [q] to stop, [?] for help
frame=    0 fps=0.0 q=0.0 size=       0kB time=00:00:00.00 bitrate=N/A

The video encoding starts, however, if I remove -ss and -t flags. But my purpose is to split the video in two parts so that does not solve the problem.

How long are you waiting? When ss is specified as an output option, ffmpeg goes through the rigmarole of encoding all frames but discards packets with timestamp less than the start time. As a test, specify a low ss like 5 seconds and see if fps switches to non-zero value.

And in place of vbr, use -q:a

Why -crf 8? Why did you choose that value?

-crf 8 gives me (almost) "visually lossless" quality, good for storing many cut videos to combine them later in a video editing program.

The way you are specifying the -ss 00:03:30 is currently as an output argument.  Doing it this way causes FFmpeg to decode the file from the beginning of the file, and then dump frames until it reaches -ss 00:03:30.  This takes much longer than specifying the -ss 00:03:30 as an input argument.
Instead, try this command:
ffmpeg -ss 00:03:30 -i "a.mkv" -c:v libx264 -preset slow -crf 8 -c:a libfdk_aac -t 00:01:30 "h.264/a1.mp4"

