To intentionally lose in arena defense the only hero I deploy is a level 20 angel. I recently consumed the angel to make space for more heroes but she is still standing guard on defense when I view reports. Seeing the angel again made me think of better times and brought a tear to my eye.
I copied this from a castle clash wiki, it answers your question:
You get more honor for winning a battle against an oppenent than losing (by 34) but you also get more per hour if you are at a higher rank. So depending on the highest rank you can achieve, it may be more beneficial to lose battles defensively (like by putting only 1 hero into the defense team) so your always facing easier opponents and gaining more honor on wins against them. When your off for a long period of time, switch back to your best defensive team so you can secure your rank and keep getting the higher hourly honor while your away.
One formula to help decide when to do this is: X > Y - 68
X = hourly honor when your losing defensively on purpose, Y = hourly honor when your trying to go for the highest rank. While this formula is true, you are better off defensively losing until you get stronger heroes. So if your hourly honor when losing (X) is 50, you should lose defensively on purpose only if your winning hourly honor (Y) is less than 118.
This formula is only a good estimate on the cost/benefits of this action.It may not take into account all possible situations that could arise. It assumes you will always find a target to win against when your defensively losing, which may not be the case sometimes.