>> In my experience it is not the budget but the politics.
Politics are usually about budget. You really can't separate the two.
>> Is your company's security worth the expense of an additional tech? Or are office politics the reason you cannot get an additional tech?
This is an entry-level "think of the children" argument. Come back when you can express your needs for an additional tech in downtime, lost customers, etc. (i.e., money).
>> Does whomever is in charge of your technology have the authority to say "no" to requests from other departments? And the political capital to make it stick?
Surprisingly, they often DO have the authority, but they're smart enough to know that a cost center that says "no" too many times is a cost center begging to to replaced.
>> Retrofitting security is not the answer.
Unfortunately, it usually is, because replacing all systems and processes from scratch would be significantly more risky, expensive and (wall clock) time consuming.