Unfortunately these decisions they make are almost always not eligible for appeal. The
after careful consideration phrase usually implies they did a serious analysis of your fiat and crypto transactions and decided there is something they don't agree with. Perhaps excessive inward and outward movements which might suggest structured transactions. A structured transaction is a suspicious series of transfers which a bank (in this case Bitstamp) suspects might be related to money laundering.
As you can see, they asked a lot of questions. These are usually questions asked when money laundering or an AML policy violation is suspected.
If you suspect this was an unfair decision, you can escalate the matter by writing to the Luxembourg financial regulatory authorities or the Commission de Surveillance du Secteur Financier. The website is
http://www.cssf.lu/en/I suggest you continue trying to contact Bitstamp first and let them know that you will advance the matter to the CSSF if they do not allow you access to your funds. Try contacting them on their Facebook and Twitter pages. You should also PM their representative here and inform them about your intention to escalate the matter to the CSSF for arbitration or clarification.
If they have a solid case against you (for example, if there is indeed a strong suspicion of money laundering after they carefully studied your account's fiat movements) then they have a right and even an obligation to close and sanction your account (which is what the account closure is). The money you have on that account, if any, must be explained. Will they return it or not? If they are not returning it, then it's probably because they suspect your account was used to commit money laundering.
Exchanges will also close accounts if assets within that account are, after considering a balance of probabilities, difficult to ascertain as truly yours and yours alone. When money laundering is suspected, they usually consider the possibility of third parties being the true owners of some or all of the funds.
Bitstamp is not a scam exchange. They have proper audit and accountability systems in place.