How many TSI I am allowed to submit?
How many TSIs are included with my Developer Program?
  
  
  iOS Developer Program, iOS Developer Enterprise Program, and Mac Developer Program Included with each enrollment are two (2) Technical
  Support Incidents per membership year. Additional TSIs are available
  for purchase.
  Safari Developer Program. TSIs are available for purchase in either a 2-Pack for $99 USD or
  5-Pack for $249 USD. Safari Developer Program members may purchase
  TSIs in Member Center under the Programs &amp; Add-ons tab.
  MFi Program. Included with each enrollment are eight (8) Technical Support
  Incidents per membership year.
  


Source: Requesting Developer Technical Support (you need a developer account to access).