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I was encoding the Hogans Heroes Season 2 Disk 5 DVD and for a few of the titles, Handbreak indicates that "No Valid Source Found" when I select the MKV files for processing.

However, when I open the MKV in VLC it is able to play back the content. How can I fix this issue? How can I export them to a valid format for Handbreak?

What does MediaInfo say about your .mkv files? Is there anything unusual about them?

Were your .mkv files created with MakeMKV from your Hogan's Heroes DVDs?

Yes the MKV was made from the DVD.

Here is what MediaInfo states:

General
Unique ID : 281330661397688393620486807081247570313 (0xD3A6508377384D67AAE09AB1F1B7F989)
Complete name : /Users/{username}/Movies/HOGANS_HEROES_S2_D5/Hogans_Heroes_S00E13_Bob Crane Radio with Richard Dawson & Chad Everett_T17.mkv
Format : Matroska
Format version : Version 2
File size : 22.5 MiB
Duration : 16 min 14 s
Overall bit rate : 194 kb/s
Encoded date : UTC 2022-10-10 20:19:59
Writing application : MakeMKV v1.17.1 darwin(x64-release)
Writing library : libmakemkv v1.17.1 (1.3.10/1.5.2) darwin(x64-release)

Video
ID : 1
ID in the original source medium : 224 (0xE0)
Format : MPEG Video
Format version : Version 2
Format profile : Main@Main
Format settings : CustomMatrix
Format settings, BVOP : No
Format settings, Matrix : Custom
Codec ID : V_MPEG2
Codec ID/Info : MPEG 1 or 2 Video
Duration : 33 ms
Bit rate mode : Constant
Bit rate : 35.0 Mb/s
Maximum bit rate : 8 000 kb/s
Width : 720 pixels
Height : 480 pixels
Display aspect ratio : 4:3
Frame rate mode : Constant
Frame rate : 29.970 (30000/1001) FPS
Standard : NTSC
Color space : YUV
Chroma subsampling : 4:2:0
Bit depth : 8 bits
Scan type : Progressive
Scan order : Top Field First
Compression mode : Lossy
Bits/(Pixel*Frame) : 3.375
Time code of first frame : 00:00:00:00
Time code source : Group of pictures header
Stream size : 141 KiB (1%)
Language : English
Default : No
Forced : No
Original source medium : DVD-Video

Audio
ID : 2
ID in the original source medium : 189 (0xBD)128 (0x80)
Format : AC-3
Format/Info : Audio Coding 3
Commercial name : Dolby Digital
Codec ID : A_AC3
Duration : 16 min 14 s
Bit rate mode : Constant
Bit rate : 192 kb/s
Channel(s) : 2 channels
Channel layout : L R
Sampling rate : 48.0 kHz
Frame rate : 31.250 FPS (1536 SPF)
Compression mode : Lossy
Stream size : 22.3 MiB (99%)
Title : Stereo
Language : English
Service kind : Complete Main
Default : Yes
Forced : No
Original source medium : DVD-Video

Text
ID : 3
ID in the original source medium : 189 (0xBD)32 (0x20)
Format : VobSub
Codec ID : S_VOBSUB
Codec ID/Info : Picture based subtitle format used on DVDs
Duration : 11 ms
Bit rate : 876 kb/s
Frame rate : 87.891 FPS
Count of elements : 1
Stream size : 1.18 KiB (0%)
Language : English
Default : Yes
Forced : No
Original source medium : DVD-Video

There are a couple things a little unusual in that output. For example, here's the video section of an episode of the TV Show Long Way Round that I happened to have handy.
Notice, the Duration in my example is listed as 44 min 4 s, which is how long the episode is. Yours is listed as 33 ms, which is quite short. There are a couple of other unusual things as well; Bit rate for instance. Perhaps most importantly, the file size is listed as only 22.5 MiB, which is probably too small for a whole episode.

I would guess there was an error while the episode was being ripped. Perhaps try ripping it again.

The portion was a static screen with audio playback. It was from the Special Features section which had an old radio show recording of two of the stars.