The Question was, "When does refinancing make sense?"

The only real way to answer your question is to work the numbers.
This issue is that most people have equity in their home that is really not doing them any good.
I.e. (your home appreciates at the same rate regardless if you own it outright or it's 100% financed.) So The deal is here you are going to want to make sure that you are out of debt first..
i.e pay down all credit cards and get money into an account earning a rate of return as soon as possible..

See the difference is this.. The interest you pay on home loans is simple interest.. Ie. 6% of $100,000, interest only the payment will be $500 / month.. Unless the rate changes. (not to mention, it's also tax deductible) Now the interest you receive on money that's invested is compounded interest.. So let's just say for the ease of math.. You have a loan for $200,000 at 6% with an interest only loan your payment = $1000 Now because it's tax deductible, given a federal tax bracket of 25%, your effective actual rate is 4.5%.. So now, let's say instead of paying principle on that loan,(which would only be $199 a month on a normal 30 year loan.
You take that at put it in a investment account earning a rate of return of 7%...
In 5 years your investment account will be worth = $14,529.09 If you were to make that principle payments on your loan you would of paid down only $13,891 of your principle..
You would think not that big of a deal. Except that, in those 5 years you have created liquidity..
That would carry you if you loose your job, get disabled, want to make an investment etc.
If that money is stuck in the value of your home, you have no ability to access it if the worst occurs.

Also, if you are accumulating equity outside of your home you are also keeping alive the best tax deduction that most of us have.. (our mortgage). If you are paying it down, you are killing it..
Why would you do that, when you are working and need all the tax deductions that you can get?

Now let's look in 10 years.
In 10 years.. Same investment strategy..
$199/month in account
You have a loan balance of $200K, Still getting the $12K a year write off.
Now you have $34,844 in a liquid reserve account...
(imagine if this money was going in your 401K and you were getting it matched from your firm.) Net worth = $424,989

Vs. putting the money toward your principle.
10 years.
Loan amount $167,371
Now yearly mortgage interest deduction is lowered to $10,042 No liquidity..
Net worth = $422,724, assuming 7% appreciation on the home.

Now this difference is vastly compounded if you continue to take equity out of your home as soon as it builds up and put it in the reserve account..
Let's say at year 5.. You decide to do a refi and take cash out..
House would be worth $420,766...@ 7% appreciation..

Increase your loan to 80% LTV for a loan amount of $336,613..
Now your tax write off's are a $20,196/year..
Vs. the paying principle version at year 5 of only $11,166 in mortgage interest..
Now if you took that money minus fee's and put that into your reserve account..
Five years later you would have $198,538 in your liquid reserve account..
The house is worth $590,146..still assuming 7% appreciation.
Your overall net worth is estimated @ $457,562..

Compare that to year 10 with just your 30 year fixed loan.
House is also worth $590,146
Loan amount is down to $167,371..
No liquid reserves,
Annual mortgage tax write off is down to $10,042 Total net worth is estimated @ $422,755..
That's $25K less than the other option...

However, what about the increased payment on the higher loan amount?
Well, that's easy..
Your total payment goes from $1199 on the 30 year fixed to $1656..on the interest only loan.
Now the $1199 of that by year 10 that's a $10,042 mortgage interest write off on your taxes At the 25% tax bracket, that equals $2510 back at the end of the year Vs. the higher loan amount with a $20,196 total mortgage interest write off At the 25% tax bracket, this equals $5049 back at the end of the year..
So you still come out ahead..

Now what if the value of your house goes down?
Let me tell you this.. Your are going to be really happy you took that money out..
Say your appreciation per year actually drops to 1% for 5 years after you took the $130K out..
In 5 years you have $198,538 in your liquid reserve account.
@ 1% appreciation your house goes to $442,229 from $420,766 You maintain your $20,196 mortgage interest write off and your overall net worth Is estimated at $309,645..

Vs. the 30 year example, house appreciates @ 1% Your house will still be worth $442,229 from $420,766. However, you loan amount is down to $167,371..
You have no liquidity. Your tax write offs are down to $10,042 / year And your net worth is only estimated @ only $274,858.. That's a $34,700 difference in 5 years. Imagine 10.

Now what if you loose your job and you have no income?

Which option would you of rather of taken?
Which option is safer?..
The lower mortgage with the lower payment and no money to make it?
Or the higher mortgage with enough liquidity in order to ride out until you get a new one?
See financial planners have been using this mantra for years..
Diversify, diversify, diversify,,
Mortgage planners have finally caught on..
See I told you this was a long answer..

In financial planning you should have 4 goals..

1) get a reserve account: (This is for things called life.. Ex. Car breaks down, need to go to the doctor.. Whatever..)The whole purpose of this account is develop the habit of accessing this account instead of your credit cards.. Why? Developing wealth is almost all about good financial habits.. It's virtually impossible to out earn-bad financial habits..)

2) Pay off all revolving debt: This way you get to decide what you do with your money every month instead of the creditors..

3) Big liquid reserve account: Make sure it's diversified, safe, earning a rate of return.. All those good financial words.

4) Pay off your house: However, new definition of pay off your house is have enough money in account #3 to pay off house you wanted to however, don't do it.. Does not make sense.. Need the write offs..

These steps should be followed in this order..
Any money in number 4, should only be there if the other 3 have already been done..
Otherwise your plan will not be efficient or effective.

So that would be the long answer to why people would refinance their house, even to a higher rate if need be.. Remember all rates of return are relative.. Meaning, even if home loan rates go to 12%, market returns will be 15%... Check it out, it's historically accurate..
If you want to know more..there are so many books out there..

Read:
Missed Fortune 101, Doug Andrews
Borrow Smart, Retire Rich, Todd Kendall
Millionaire Mortgage Planner, Steven Marshall Last chance Millionaire, Doug Andrews

Truly the list goes on and on..