Setup:

• You have boots that use the movementSpeed attribute
• You are wearing and holding the boots

Place in a command block and activate it to obtain test boots:

give @p minecraft:leather_boots 2 0 {AttributeModifiers:[{AttributeName:"generic.movementSpeed",Name:"generic.movementSpeed",Amount:0.5,Operation:0,UUIDLeast:894654,UUIDMost:2872}]}

When you switch to another slots that does not have the boots, The speed attribute is removed even though you are still wearing the boots. Only way to correct the issue is to then take the boots off and put them back on to apply the speed attribute again.