You should also save another state to indicate whether you have already used up your ability to delete an element or not. Something like:

$$$dp[i+1][b]=dp[i][b]+1$$$, for $$$b\in \{0,1\}$$$, if $$$a[i]<a[i+1]$$$

$$$dp[i+1][1]=dp[i-1][0]+1$$$, if $$$a[i-1]<a[i+1]$$$

return $$$max(dp[n][0],dp[n][1])$$$