An expression for trying to futilely apply old methods that once worked

In the software company I work for, we call that:

"paving the cow path"

That's when a client wants to use the software but doesn't want to change any of their old, established practices that the software may streamline for them because they or their staff are resistant to change.

On the website AgileConnection.com, Jim Highsmith offers this definition:

Summary: In the IT world, "paving cow paths" means automating a business process as is, without thinking too much about whether or not that process is effective or efficient. Often business process automation initiatives require figuring out entirely new ways of doing business processes–impossible prior to automation (for example, work flow automation and digital image processing)–defining more effective and efficient process highways. In this week's column, Jim Highsmith warns that when we pave the cow paths and ignore the highways, we do a disservice to our customers.

The best term I've heard used for that situation is "Cargo Cult".

The term cargo cult, as an idiom, originally referred to aboriginal religions which grew up in the South Pacific after World War II. The practices of these groups centered on building elaborate mock-ups of airplanes and military landing strips in the hope of summoning the god-like airplanes that had brought marvelous cargo during the war.

The late Nobel laureate Richard Fenynman popularlized the term for Science done that way in one of his autobiographies, but it has been taken up by the programming community.

Cargo cult programming is a style of computer programming that is characterized by the ritual inclusion of code or program structures that serve no real purpose. Cargo cult programming is typically symptomatic of a programmer not understanding either a bug he or she was attempting to solve or the apparent solution (compare shotgun debugging, deep magic). The term 'cargo cult programmer' may also apply when an unskilled or novice computer programmer (or one not experienced with the problem at hand) copies some program code from one place and pastes it into another place, with little or no understanding of how the code works, or whether it is required in its new position.

It has apparently been used a couple of times in Economics too, to describe attempts to advance economies by blindly emulating observable features of other successful economies.

Jesus would call it "putting new wine into old wineskins," or repairing an old and threadbare garment with a brand new patch, neither of which is a good idea.

As for the first analogy, here's something of historical interest (perhaps) which applies quite nicely to your question. It's from a sister website on the Stack Exchange called biblical hermeneutics beta, and the paraphrase was submitted by "metal" today:

"Summarizing Hastings Dictionary of Christ and the Gospels entry on wine bottles:

In ancient Israel, the grapes were pressed in the winepress and left in the collection vats for a few days. Fermentation starts immediately on pressing, and this allows the first 'tumultuous' (gassy) phase to pass. Then the must [that is, the word which denotes the crushed grapes, skins, seeds, stems, and juice, altogether] was put in clay jars to be stored, or into wineskins if it was to be transported some distance.

The wineskins were partially tanned goat skins, sewn at the holes where the leg and tail had been. The skins were filled with must (partially fermented wine) from the opening at the neck and then tied it off.

If one puts freshly pressed must directly into the skin and closes it off, the tumultuous stage of fermentation would burst the wineskins, but after this stage, the skins have enough stretchiness to handle the rest of the fermentation process. However, skins that have already been used and stretched out ('old wineskins') cannot be used again since they cannot stretch again. If they are used again for holding wine still in the process of fermenting ('new wine'), they will burst."

In like manner, people who are resistant to new ideas or to a new paradigm, are reluctant to let go of the "tried and true" paradigm and embrace the "untried and untrue"--perhaps even needlessly revolutionary--new paradigm. The "revolutionary" heliocentric paradigm and the "old" geocentric paradigm of the planets is one example of how the new and the old conflict, sometimes for centuries, until one theory replaces the other and becomes the new status quo.

New wine needs new wineskins, and a new patch is not compatible with an old garment. The new and the old are like oil and water; they need an emulsifier. That emulsifier is the new idea, though combining the oil, the water, and the emulsifier requires a bit of vigorous shaking!

I would be likely to describe that person as dyed-in-the-wool. Someone who is dyed-in-the-wool has very deep-seated opinions and is very unlikely to change them or try something that may challenge their beliefs. In the scientific research industry, we use that expression to describe some researchers who continue to rely on antiquated and outdated analysis techniques, ignoring faster, more reliable and more comprehensive modern techniques (even though some of these have been around for about 30 years).