I am trying to play an MP3 clip in a continuous loop for a sound effect. There is a small empty space at the start, about .05 sec. This makes a noticeable blip when the sound loops, messing up the continuity of the sound. I delete it in audacity (first I was using 2.0.5, now on 2.4.1 problem persists). Looking at the waveform the empty space is deleted but when I save and reload the file, it is back. Is this a bug or something inherent in MP3 format? I seem to be able to save as WAV without the blip. Thanks. 
It’s inherent in MP3 format.
Formats that don’t have this limitation include: WAV, FLAC, OGG, AIFF.
Thank you, Steve!
This issue is fixed for the soon to be upcoming 2.4.2 release.
This is what it says in the “What’s New…” section in the 2.4.2 manual
MP3 exports and imports without padding
Audacity now supports LAME’s gapless playback info, allowing MP3s to be exported and imported without additional padding.
Other applications that support the LAME tag, for example audio player applications, will be able to read MP3 files exported by Audacity without the padding.
WC
There’s a big and important caveat to that:
An MP3 exported from Audacity may loop (almost) seamlessly in Audacity, but there is no guarantee that it will loop seamlessly in other applications.
If the other application does not support the LAME “gapless playback info” metadata, then there will still be a small empty space at the start.