I want to write an assertion for checking that the data stable for 16 clock cycles and continue the checking for the next 16 cycles and so on.?How can i write this?

You will have to add a term to the antecedent on every change of uart_tx_o, otherwise your assertion would fire a cycle after every change of uart_txt_o

Try this:

property framecheck
  disable iff(rst || !tx_frame)
  tx_frame && $change(uart_txd_o) ||-> ($stable(uart_txd_o)[*15]);
endproperty