could it be 'even though'? It is slightly different from however. It would explain that they were able to do something that is normally your job, or something that you manage.

The first answer is right as well, but here are some slightly different possibilities. I think you mean.....The last time I did this it didn't seem to be a problem. Or...There didn't seem to be a problem the last time I did it/this.

A letter for my new employer

Hello. My name is Tom and I am supposed to be starting work at your office next week. I am writing this letter to ask you about changing the starting date of my new job.

You have arranged this job for me but my working visa for this country has not been issued yet.
Although I have asked the working visa department what is going on, they have still not answered.  I have decided to return to my country to apply for another valid working visa. I am sure that this is the best way to start my new career with you.

For that reason, I probably cannot start the job until the end of this month. I am sorry to cause you any inconvenience. In hindsight, I should have applied for my visa earlier. This is my fault and I would offer that you pay me half a month's wage for the first month.

Anyway, I am going to do my best when I start my new job. See you soon. Thank you.
Yours sincerely.
Tom