Cisco ASA intermittently fails to see traffic

users 
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Mikrotik -- Internet
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ASA
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ServerA and ServerB

I'm trying to troubleshoot a problem with a new Cisco ASA 5505. The network design is as above – the Microtik is the existing router, ServerA and ServerB used to plug directly into it.

ServerA has IP 10.30.1.10, ServerB has IP 10.30.1.11
The ASA is configured with no NAT, a "allow anything" firewall, and uses the microtik as its default gateway. In effect, it is currently a simple IP router; the firewall and VPN stuff will all come later once the basics are working.

Th problem is access to ServerA and ServerB is erratic – sometimes it will work, sometimes it will fail. It can fail for either one of the servers only, or both.

When it is working:
The Mikrotik logs show ping packets being sent out over the proper interface
The ASA logs show the incoming connections.

When it is failing:
The Mikrotik logs show ping packets being sent out over the proper interface
The ASA logs show nothing reaching the ASA.

This can fail for one server only (e.g.: the Mikrotik is putting out packets to 10.30.1.10 and 10.30.1.11, but the ASA is only seeing packets arrive destined for 10.30.1.11)
It can fail for one source only (e.g.: ClientA on the users network can ping 10.30.1.11, but clientB cannot)
The problem can also be seen from the mikrotik router itself; sometimes it can ping ServerA and ServerB, sometimes it can only ping one of them

What could be causing this? I can't think of any possible cause that is intermittent and could explain why the problem may occur for one destination server and not others.

edit:
Link to ASA config