Will it be fine to consume 0.0058 mA from a LiPo cell after its lowest discharge voltage of 3V has been reached?
Drawing 5.8 uA for a few days would probably be OK especially if you set the cut-off a little higher, but the problem you're likely to have with that regulator is that the quiescent current is about 30uA while shut down so it'll be higher while running, possibly in the order of milliamps (it doesn't seem to be specified that I can see).

It sounds like you may not have considered that while the AVR on the Arduino in sleep mode may only be drawing 5.8 uA the regulator will continue to draw it's usual quiescent current. There's two things I'd recommend:


For something robust there are external under-voltage protection circuits you could use. For example I found a Linear Technology application note on a LT1495 based protection circuit that draws 4.5uA.
If it's for your own / general hobby use make the setup as described and set the AVR to go to sleep at 3.1 V and make some measurements to see how fast it's dropping towards 3 V. Then you can determine a good cut-off point to use that gives you an acceptable amount of time to remove the battery before it's damaged.


They'll be a bit of compromise between the cut-off voltage and how long it can survive without being recharged, but most lithium batteries rapidly decline below 3.2 V so you probably won't be missing out on a lot of charge.