Can't write more than one byte to the SST39SF010A Flash!
Problem solved and I would like to share the solution:

Software Data Protection

This feature is available on some flashes that requires a software sequence at the beginning of each write cycle in order for a write to be performed. To enable the software data protection feature, a series of three-write commands to specific addresses with specific data must be performed. Once set, the same 3-byte code must begin each write request. This feature is permanently enabled in the flash I'm using.

So the solution is to add the following commands before any byte write operation not only the first one:

    * flash_addr1 = 0xaa;    
    * flash_addr2 = 0x55;
    * flash_addr3 = 0xa0;