I recently quit my job, mostly for management reasons. I found the job through a staffing agency so I was supposed to tell them. I did not because I lost my phone. I could have also e-mailed but they rarely replied to my e-mails so I assumed they had some system problems (not sure?) and gave up. A few days later, I visited them and the person in charge complained that I should contact them so I gave him my reasons mentioned above. I also told him that I left my allergy medicine inside the office. Then, he said I should have e-mailed him (???) and he cannot place me in a new job because I was unreliable. I was angry so I politely said I had an appointment and left.
Later I e-mailed him and said if he thinks I am unreliable, I am okay to accept any proposal to prove that I am reliable. I also asked him if there were problems in the e-mail system and offered to e-mail from a different account if it did not work. I gave him a list of dates I sent e-mails. He just replied that a reply was "not needed" even when my e-mails asked him questions (e.g. is it ok to take a holiday because of a family gathering I am not allowed to miss?). After I found my phone, I called him and asked "Do you have all my e-mails that I listed dates?" and FINALLY he said yes.
When I e-mailed him again 3 days ago to repeat the offer and talk about my allergy medicine, he did not reply. Yesterday, I phoned him and again he said "no need to reply" but he said he will help me find the allergy medicine.
I already know I should have gone to the office earlier and tell him if other communication methods cannot be used. This was my fault and I apologised to him about that. This was why I asked him for a proposal, or if he wanted, I can make one myself and see if he approves. But do you think there is something else I can do better? I am not very experienced with work, so I am not sure why he is completely ignoring my offer. I also never say anything that may be slightly insulting to him.
In some ways, I want to quit using the staffing agency. But I am not sure if I made more mistakes that led to this. I don't want to quit because it was my fault. I should repair what I do wrongly. What do you think I should do?