Here is what Bill does with NEW suppliers:
1. Before I place an order with a new supplier, I have already check with them that they ship my items quickly. This is a bit of a dance. You are just getting to know each other and looking to establish a relationship.
2. Once a place an order, I ask them to please ship the item as quickly as possible and update the tracking code in AE or by AE messenger so I can update my eBay account. This is not automated on their end, they have to do so somewhat manually.
3. If I am getting close to my handling date, I start hounding them twice a day if they have shipped and if so, what is the tracking number. I remind them I am a dropshipper and can bring many orders but need them to ship quickly.
4. You can also ask them for their WeChat name and/or email to communicate this way.
So, what to do now? Start hounding them, be nice, but be firm that you need them to ship immediately otherwise this will damage your relationship with them and you may not order again from them. As well, if they don't ship, you will be cancelling the orders you currently have with them.
Use 7th grade language, no contractions (i.e. can't, won't, etc.). This gets translated into Chinese. Be NICE!