Here, a longer "Title" process on a Short Sale usually involves issues on Title that are liens, but not necessarily property related debts. These include any judgments/liens for taxes that are not property taxes or judgments for other types of legal, not property related, disputes. So "how long does Title Search take?" is not usually as relevant as how long does it take to sufficiently clear the exceptions on Title, and to the seller's satisfaction and the buyer's satisfaction.
It is not uncommon in a short sale, as example, for a Federal Tax Lien to appear...and sometimes right before closing when you think everything is a GO. For some people that lien is "lifted" to allow for the closing. Other sellers will not agree to it being lifted and want it paid off, and the lienholder does not agree with paying it off from the sale proceeds, and taking what is left after that payment.
How long it takes to clear the title is different for each house and dependent on what is revealed, vs the time of "the search" process. If it is a normal sale with only RE taxes and Utility Bill issues, that is not usually a problem. But I have had several that were long as to process due to State and Federal Tax lien issues that were not RE property related, a well issue on Title that needed to be declared "irrigation only", a lawsuit-judgment on the property related to a previous car damage issue, etc.
What is "on" Title is more the issue than the time to do a "search" of Title issues. The final lienholder approval and terms of that approval is something that happens between a seller and their lienholder, and requires the seller's signature of that approval and terms. It is not uncommon for everyone to agree on the short sale price...but not the terms as to what is to be paid off or what type of forgiveness is being granted to the seller on those liens. For condos, it is often many months and sometimes even years of back condo dues showing as a lien on Title. These issues are often resolved without the buyer's involvement. In some cases the buyer is asked to pay them in whole or in part.
Because new items can appear on Title after the initial Title Search, it is usually best to close as soon as possible after lienholder approval and escrow clears title...vs your 30 day loan process beginning "at lienholder approval". New liens can, and often do, get recorded while it is still in the seller's name during escrow.
There will be updates to Title throughout the process. It is not a "once and done" search.
These issues could also come up if it is not a short sale, but in my experience they rarely come up on a "normal" sale. and often come up in a "short sale". Could simply be my anecdotal experience and not reflective of all closings, but my best guess is that is the case for most real estate transactions.
If the issue that pops up pertains to vesting, it could take months.
You raise a good point though about how the report will be periodically updated. It is important to review those updates because they can affect the ability to sell. I once looked over a matter where the agent received four updates, each of which would have affected the ability to sell, but the agent ignored them.