ては

ては is the て form of a verb or adjective, + は. It is a pretty hard piece of grammar to define. It has a variety of usages and is somewhat common.
Generally speaking it breaks down into 3 categories:

• たら – Bad result, Certain Result, Advice
• Contrastive は – てはみる、てはいられない,
• Repetition

It is best to rely on your own instincts with this, but the meanings are covered below.

As たら

”たら”
Verb/Adjective/Noun て form + は

The most common meaning of ては is たら. It can be used for:

A hypothetical bad thing – When/if that happens, its bad.
Advice – たらどうだ
Factual result –  Closer to と than たら, but put here for simplicity. 

This means ては can be used in most situations that たら can, except for “Surprise”. 
It also cannot be used for a hypothetical, non factual good result. I.E.:
勝っては皆は喜ぶ.✖

Hypothetical bad thing

It would be bad if…
Hypothetical + Word ては + bad thing

This is the same ては from てはいけない and てはならない
It must have a bad result.

Examples

• 損失が出ては大変なことになる – If there’s a loss, its going to be a big problem.
• それを触れては三日も苦しみ続けるよ – If you touch that, you’re going to suffer for 3 days.
• 彼が出てはもう価値もはない – Now that he’s gone out, there’s no chance of winning.

Advice

How about…
Word ては + どうだ

This meaning is mostly used with どうだ.
It is the same as たらどうだ。

Examples

• 話してはどうだ？ – What if you just talk about it?
• 先生に聞いてはどうだ？ – Why don’t you ask the teacher?
• 彼女に頼んではどう? – What if you ask your girlfriend? 
  
  

Factual result

If X, then Y
Word ては + Guaranteed result

This meaning is used for when some set of circumstances will always produce a result.
In order to always produce a result, the statement will probably be factual.
This pattern is mostly used as a warning, so also tends to have negative results.

Examples

• 遊んではよい成果が得られない (Weblio) – If you play you wont get a good result. 
• 物を盗んでは逮捕される – If you steal, you will be arrested.
• 物をいつも忘れては大変だ – Always forgetting things is tough. 

ていては

If you keep doing/If it keeps being then…

This is just the factual result meaning of ては, but connected to the progressive form of a verb.
It means “If X keeps doing/being” then Y.

Examples

• 相手を侮辱していては痛い目に合うよ – You’re going to be sorry if you keep insulting your opponent.
• 先生を無視していては怒られるよ – If you keep ignoring the teacher you’re going to be yelled at.
• 授業をさぼっていては卒業できないよ – If you keep skipping class you won’t graduate.
• その態度を取っていては友達ができない – If you keep taking that attitude you won’t make any friends. 

As Contrastive は

Emotional Reason

Now that X, (For emotional reason) Y

This usage is very similar to からには, except that it used with things that create an emotional reason to do something. This is usually pride or social face.
That’s probably confusing, so please look at the examples.
This is also similar to たら.

• そこまで言われてはもう引けない – Well, since they’ve said all that, I can’t back down now. 
  (If they hadn’t said that though..)
• 皆の前で約束してはもうしなければならない – Since I promised in front of everyone, I have no choice but to do it.
• これだけやっつけられては反論する気も起きない (Weblio)- Having been beaten up this much, can’t even try to argue. 

てはいられない

Can’t be doing X

てはいられない means “can’t be doing” it is the opposite of ず/ないではいられない
There is an implication of having something more important to do.

Although tempting to use いては, this is incorrect because there is already an いる (いられない)

Examples

• 油を売ってはいられない – Can’t be wasting time here. 
• ここで話してはいられない – Can’t be talking here.
• 落ち着いてはいられない – I can’t be calm right now.
  
  

てばかりはいられない

Can’t only be doing X

This is a variation of てはいられない, with ばかり falling in between て and は。
The meaning is a straightforward combination of ばかり (only) and てはいられない;
Except that it is usually used for actions that take place over a “long” period. (This could be 5 minutes)
Like てはいられない, It also implies some more important task to do. 

• 寝てばかりはいられない  – You can’t just be sleeping all the time.
• 話してばかりはいられない – Can’t just be talking. (We have things to do).
• 文句を言ってばかりはいられない – Can’t just be complaining all the time. 

てはみる

I’ll try but…

This ては is the easiest, as its just contrastive は inserted after a て.
It adds an implied object of comparison.
It is used to express a lack of confidence in the action being done.
This pattern likes to pair with みる

Examples

• 書いてはみる – I’ll try to write it but... I might not write it well (書くけど、上手に書けないかも)
• やってはみるけど、約束できない – I’ll try, but I can’t promise anything
• 調べてはみるが、期待できない – I’ll try to look it up, but I’m not hopeful. 

Repetition

Many times/Every Time
Verb + ては + Verb

This is actually N1 Grammar.
This pattern links 2 verbs that are done repetitiously, or are always done together.
This can be both “Many times” and “Every time”.
Its mostly a written pattern and kind of rare.

This pattern is occasionally repeated.

Examples

• 酒を飲んでは歌いだす – Every time he drinks, he starts singing.
• 食べては寝る – Eat and sleep (repeatedly).
• 本を読んではメモを書く – Repeatedly reading the book and writing notes. (Reads, then writes notes, then reads…)
• 彼女を見てはほほ笑む – Smile every time I look at her. 
• 雪は降ってはやんで、降ってはやんだ。- The snow fell and stopped, fell and stopped.
• 痩せては太って、太ってはやせるのを繰り返した
  He kept loosing weight and gaining weight, gaining weight and loosing weight.