IELTS re-mark or re-evaluation may be possible for writing or speaking if you have the time and money.
By the way it is officially called an Enquiry on Results.
Whether you should request a re-evaluation of your IELTS test depends on your circumstances. You might just be lucky if you just need only a 0.5 change. Unlike what you think, speaking is very reliable skill. Score does not change as much in speaking section. On the other hand, there are higher chances of seeing success in writing section. If you have prepared for your test effectively and you are confident that the test went well based on your mock tests, you would probably get a high band score.
Remember, it costs almost as much money as it costs to register for the test.
Official sites say that it takes about 28 days.
Can you wait a month? and can you spend about USD 200 (depends on the country you are from). If your answer is yes, then go for re-evaluation. If you need more than 0.5 in listening or reading, I would recommend you give it another try and register for a new date. It is very unlikely that you will see any difference in score for listening and reading.
I have seen only one success story where someone reported getting 1.5 score increase.
IELTS does not provide any details on what percentage of re-evaluation is successful. Every case is different. Hence, it is very difficult to tell if you should request for re-evaluation or not.
Before making any decision, you should consider following facts.
If there is a difference of 2 band scores between two sections, you will get an automatic re-evaluation in your local test center. This means that an examiner and a senior examiner have already assessed your test and it is unlikely that a third examiner will have a different opinion.
You must apply for an enquiry into your results within 6 weeks from your test date.
You can choose to have one section or all sections of your test re-evaluated.
Your paper will be sent to a IDP or BC Head Office i.e. Cambridge or Melbourne. Your paper will be marked again by a senior examiner and they will not be told your original score. So, it will be completely unbiased.
The re-evaluation process takes about a month.
If your score changes, the fee is refunded.
Whatever may your decision be, I wish you best of luck.