Using Microchip's dsPIC33E USB Starter Kit
I think the putrsUSBUSART(); function is probably non-blocking and has a check for the peripheral being busy. When you try to send the second string it checks and finds the peripheral is busy so simply skips.
I recall another "sendUSB" type function working in this way in the USB libraries.  

For a quick test of the above, try adding a delay between the two function calls to see if it solves the issue (this is not a permanent solution - there is probably a function to check for this but this should do just to check)   

From what I can see, the dsPIC33F starter kit relies on another PIC with a USB peripheral to do the USB comms (AFAIK none of the dsPICs have a USB peripheral)
It also looks like the demo firmware is set up to emulate a COM port for serial comms. I couldn't find any documentation for the code, but I did find this:  


  The instructions for this demo can be found at C:\dsPIC33E PIC24E USB
  Starter Kit Demo\Documentation\Getting Started\Getting Started -
  Running the Device - CDC - Basic Demo. See the Running the Demo
  section.


I'm assuming all the necessary documentation is going to be in the "Documentation" folder. It should have details of the functions used in the demo application, so you can check how they work. You could also just check the function code itself.