I bought something from the vendor's but I haven't received anything.

Any of the following could cause delivery to fail silently:

1. You were in busy mode.
2. You had inadvertently put Lulu Ludovico on your mute list.

•  You might have done this when when you pressed "Mute" instead of "Discard" for any of Lulu's notecards when you clicked the vendors.
  
• Check by clicking on the SL Menu: View > Mute List.

3. SL communications failure.

To fix, IM Lulu Ludovico with details of what you bought. Remember, if Lulu is (still) on your mute list, you will not be able to receive her replies either.