OS X Samba file sharing continuously asks for password
Samba passwords are managed separately from your regular account password. Have you set-up your user to enable samba sharing in the options menu? You need to do it once otherwise the login won't work.

In the File Sharing preference pane tick the checkbox next to the user you want to enable file sharing for and a window will pop-up asking you to authenticate.

As soon as this is done you should be able to login from your android tablet.



UPDATE

The root cause of the issue might be that 10.9 uses a new SMB2 Stack completely written by Apple (SAMBA is not used anymore). Apple's SMB2 implementation is not compatible with many other SMB2 NAS products on the market today while Windows 7, 8, and 8.1 work just fine. In short, it's an Apple bug.

As a workaround you can force OSX to use SMB1 instead of SMB2 using a configuration file:


Open up the Terminal
Paste the following line followed by a return key (command should be one single line)

echo "[default]" >> ~/Library/Preferences/nsmb.conf; echo "smb_neg=smb1_only" >> ~/Library/Preferences/nsmb.conf


Explanation:


A file called nsmb.conf is created in your home directory at the path ~/Library/Preferences/
It adds the lines to force the use of SMB1 protocol instead of Apple's SMB2 (this is slower but more stable)