How many consecutive descending numbers in my number?
JavaScript (ES6), 56 bytes
A port of ArBo's Python answer is significantly shorter. However, it fails on some test cases because of too much recursion.

f=(n,a=0,c=0,s)=&gt;a&lt;0?f(n,a-~c):n==s?c:f(n,--a,c+1,[s]+a)

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JavaScript (ES6), 66 bytes
Takes input as a string.

f=(s,n=x='',o=p=n,i=0)=&gt;s[i++]?o==s?i:f(s,--n,o+n,i):f(s,p+s[x++])

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Commented
f = (               // f = recursive function taking:
  s,                //   s = input number, as a string
  n =               //   n = counter
  x = '',           //   x = position of the next digit to be added to p
  o = p = n,        //   o = generated output; p = prefix
  i = 0             //   i = number of consecutive descending numbers
) =&gt;                //
  s[i++] ?          // increment i; if s[i] was defined:
    o == s ?        //   if o is matching s:
      i             //     stop recursion and return i
    :               //   else:
      f(            //     do a recursive call with:
        s,          //       s unchanged
        --n,        //       n - 1
        o + n,      //       (n - 1) appended to o
        i           //       i unchanged (but it was incremented above)
      )             //     end of recursive call
  :                 // else:
    f(              //   this is a dead end; try again with one more digit in the prefix:
      s,            //     s unchanged
      p + s[x++]    //     increment x and append the next digit to p
    )               //   end of recursive call