Part of the solution is to use the /stats command to count the number of arrows in a players inventory using the /clear command, and set that result to a scoreboard objective for the player. Then it's pretty straight forward command-block-fu to give arrows when needed, as well as take them away. Let's see how I did it.
First things first, though, I'm doing this in 1.9, but the commands will work fine in 1.8, with a little adjustment and a 20Hz fill clock.
We need 2 scoreboard objectives: the arrow count (which you've named ArrowN, so I'll keep that in my example), and a timer variable.
/scoreboard objectives add ArrowN dummy
/scoreboard objectives add Timer dummy
Next, we need a chain of command blocks, starting with a repeating command block, and followed by several chain command blocks. Set the repeating command block to "Needs Redstone", at least for now, and the rest to "Always Activate". The first two commands, in order, are:
/scoreboard players remove #Timer Timer 1
/clear @a minecraft:arrow -1 0
#Timer is a dummy player that will never show up in scoreboard displays, and he will keep track of when to hand out arrows. It might be a good idea to initially set his Timer score to 40, but that's not strictly necessary. The second command will count all the arrows someone has in their inventory, independent of the number of stacks. Unfortunately, this doesn't do much for us until we get that count into the scoreboard. To do this, stand on the command block and enter the following command (through chat):
/stats block ~ ~-1 ~ set QueryResult @a ArrowN
So, whenever the clear command gets run, the count that it finds will be placed in that players ArrowN score.
The next three commands manage the 2 second timer and dole out the arrows. In 1.9, the first is unconditional, while the other 2 are conditional. For 1.8, you can use comparators off each side of the first command block, but this is a little inelegant.
/scoreboard players test #Timer Timer * 0
/scoreboard players set #Timer Timer 40
/give @a[score_ArrowN=1] minecraft:arrow
The first command tests to see if the timer has reached 0, and if so, resets it (the second command) and gives all players an arrow if they have at most 1 arrow already (the third command).
Now, we just need to remove arrows from people who have too many. These commands are all unconditional so that they run every game tick:
/clear @a[score_ArrowN_min=3] minecraft:arrow -1 1
/clear @a[score_ArrowN_min=12] minecraft:arrow -1 9
/clear @a[score_ArrowN_min=66] minecraft:arrow -1 54
These three commands will remove a total of 1 arrow if the player has between 3 and 10, 10 arrows if they have between 12 and 66, and a whole stack if they have 66 or more. You can expand on this (and add finer intervals) if you find arrows aren't being removed fast enough, but it should take less than a second in most cases.
It sounds like "Test" is not a real player.
The problem in this case is that target selectors like @a[...] can only resolve / find entities that exist somewhere in the world and are loaded.
This means that while you can change the scores of fake or offline players (scoreboard scores are stored in scoreboard.dat rather than playerdata) by specifying their name directly, i.e.
/scoreboard players set Rayset Score 29
You can not use target selectors unless there is an entity to resolve.
If an entity exists, your command is correct. @a[score_Score_min=1] resolves all player entities with a Score score of at least 1.
Best Answer
It does appear that this is due to a bug.
I don't know if there's an alternative, but it may be possible to run a function, when a player takes any kind of damage, and then check if the player has absorbtion.